366224
The value of \((\vec A + \vec B) \times (\vec A - \vec B)\) is
1 \(0\)
2 \({A^2} - {B^2}\)
3 \(\vec B \times \vec A\)
4 \(2(\vec B \times \vec A)\)
Explanation:
\((\vec A + \vec B) \times (\vec A - \vec B) = \vec A \times \vec A - \vec A \times \vec B + \vec B \times \vec A - \vec B \times \vec B\) \( = 0 - \vec A \times \vec B + \vec B \times \vec A - 0\) \( = \vec B \times \vec A + \vec B \times \vec A = 2(\vec B \times \vec A)\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366225
The vectors from origin to the points A and B are \(\vec A = 3\hat i - 6\hat j + 2\hat k\) and \(\vec B = 2\hat i + \hat j - 2\hat k\) respectively. The area of the triangle \(OAB\) be
1 \(\frac{5}{2}\sqrt {17} \) sq.unit
2 \(\frac{2}{5}\sqrt {17} \) sq.unit
3 \(\frac{3}{5}\sqrt {17} \) sq.unit
4 \(\frac{5}{3}\sqrt {17} \) sq.unit
Explanation:
Given \(\overline {OA} = \vec a = 3\hat i - 6\hat j + 2\hat k\,\,{\rm{and}}\) \(\overline {OB} = \vec b = 2\hat i + \hat j - 2\hat k\) \(\therefore \;\;(\vec a \times \vec b) = \left| {\begin{array}{*{20}{c}}{\hat i}&{\hat j}&{\hat k}\\3&{ - 6}&2\\2&1&{ - 2}\end{array}} \right|\) \( = (12 - 2)\hat i + (4 + 6)\hat j + (3 + 12)\hat k\) \( = 10\hat i + 10\hat j + 15\hat k\) \( = \sqrt {425} = 5\sqrt {17} \) Area of \(\Delta \,OAB = \frac{1}{2}\left| {\vec a \times \vec b} \right| = \frac{{5\sqrt {17} }}{2}\) sq.unit.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366226
Two vectors \({\vec A}\) and \(\overrightarrow B \) making an angle \(\theta \) which one of the following relations is correct?
1 \(\vec A \times \vec B = \vec B \times \vec A\)
2 \(\vec A \times \vec B = AB\sin \theta \)
3 \(\vec A \times \vec B = AB\cos \theta \)
4 \(\vec A \times \vec B = - \vec B \times \vec A\)
Explanation:
Conceptual Question
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366227
\(\vec A\,\,{\rm{and}}\,\,\vec B\) are two vectors and \(\theta \) is the angle between them, if \(\left| {\vec A \times \vec B} \right| = \sqrt 3 (\vec A \cdot \vec B)\) the value of \(\theta \) is
366224
The value of \((\vec A + \vec B) \times (\vec A - \vec B)\) is
1 \(0\)
2 \({A^2} - {B^2}\)
3 \(\vec B \times \vec A\)
4 \(2(\vec B \times \vec A)\)
Explanation:
\((\vec A + \vec B) \times (\vec A - \vec B) = \vec A \times \vec A - \vec A \times \vec B + \vec B \times \vec A - \vec B \times \vec B\) \( = 0 - \vec A \times \vec B + \vec B \times \vec A - 0\) \( = \vec B \times \vec A + \vec B \times \vec A = 2(\vec B \times \vec A)\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366225
The vectors from origin to the points A and B are \(\vec A = 3\hat i - 6\hat j + 2\hat k\) and \(\vec B = 2\hat i + \hat j - 2\hat k\) respectively. The area of the triangle \(OAB\) be
1 \(\frac{5}{2}\sqrt {17} \) sq.unit
2 \(\frac{2}{5}\sqrt {17} \) sq.unit
3 \(\frac{3}{5}\sqrt {17} \) sq.unit
4 \(\frac{5}{3}\sqrt {17} \) sq.unit
Explanation:
Given \(\overline {OA} = \vec a = 3\hat i - 6\hat j + 2\hat k\,\,{\rm{and}}\) \(\overline {OB} = \vec b = 2\hat i + \hat j - 2\hat k\) \(\therefore \;\;(\vec a \times \vec b) = \left| {\begin{array}{*{20}{c}}{\hat i}&{\hat j}&{\hat k}\\3&{ - 6}&2\\2&1&{ - 2}\end{array}} \right|\) \( = (12 - 2)\hat i + (4 + 6)\hat j + (3 + 12)\hat k\) \( = 10\hat i + 10\hat j + 15\hat k\) \( = \sqrt {425} = 5\sqrt {17} \) Area of \(\Delta \,OAB = \frac{1}{2}\left| {\vec a \times \vec b} \right| = \frac{{5\sqrt {17} }}{2}\) sq.unit.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366226
Two vectors \({\vec A}\) and \(\overrightarrow B \) making an angle \(\theta \) which one of the following relations is correct?
1 \(\vec A \times \vec B = \vec B \times \vec A\)
2 \(\vec A \times \vec B = AB\sin \theta \)
3 \(\vec A \times \vec B = AB\cos \theta \)
4 \(\vec A \times \vec B = - \vec B \times \vec A\)
Explanation:
Conceptual Question
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366227
\(\vec A\,\,{\rm{and}}\,\,\vec B\) are two vectors and \(\theta \) is the angle between them, if \(\left| {\vec A \times \vec B} \right| = \sqrt 3 (\vec A \cdot \vec B)\) the value of \(\theta \) is
366224
The value of \((\vec A + \vec B) \times (\vec A - \vec B)\) is
1 \(0\)
2 \({A^2} - {B^2}\)
3 \(\vec B \times \vec A\)
4 \(2(\vec B \times \vec A)\)
Explanation:
\((\vec A + \vec B) \times (\vec A - \vec B) = \vec A \times \vec A - \vec A \times \vec B + \vec B \times \vec A - \vec B \times \vec B\) \( = 0 - \vec A \times \vec B + \vec B \times \vec A - 0\) \( = \vec B \times \vec A + \vec B \times \vec A = 2(\vec B \times \vec A)\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366225
The vectors from origin to the points A and B are \(\vec A = 3\hat i - 6\hat j + 2\hat k\) and \(\vec B = 2\hat i + \hat j - 2\hat k\) respectively. The area of the triangle \(OAB\) be
1 \(\frac{5}{2}\sqrt {17} \) sq.unit
2 \(\frac{2}{5}\sqrt {17} \) sq.unit
3 \(\frac{3}{5}\sqrt {17} \) sq.unit
4 \(\frac{5}{3}\sqrt {17} \) sq.unit
Explanation:
Given \(\overline {OA} = \vec a = 3\hat i - 6\hat j + 2\hat k\,\,{\rm{and}}\) \(\overline {OB} = \vec b = 2\hat i + \hat j - 2\hat k\) \(\therefore \;\;(\vec a \times \vec b) = \left| {\begin{array}{*{20}{c}}{\hat i}&{\hat j}&{\hat k}\\3&{ - 6}&2\\2&1&{ - 2}\end{array}} \right|\) \( = (12 - 2)\hat i + (4 + 6)\hat j + (3 + 12)\hat k\) \( = 10\hat i + 10\hat j + 15\hat k\) \( = \sqrt {425} = 5\sqrt {17} \) Area of \(\Delta \,OAB = \frac{1}{2}\left| {\vec a \times \vec b} \right| = \frac{{5\sqrt {17} }}{2}\) sq.unit.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366226
Two vectors \({\vec A}\) and \(\overrightarrow B \) making an angle \(\theta \) which one of the following relations is correct?
1 \(\vec A \times \vec B = \vec B \times \vec A\)
2 \(\vec A \times \vec B = AB\sin \theta \)
3 \(\vec A \times \vec B = AB\cos \theta \)
4 \(\vec A \times \vec B = - \vec B \times \vec A\)
Explanation:
Conceptual Question
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366227
\(\vec A\,\,{\rm{and}}\,\,\vec B\) are two vectors and \(\theta \) is the angle between them, if \(\left| {\vec A \times \vec B} \right| = \sqrt 3 (\vec A \cdot \vec B)\) the value of \(\theta \) is
366224
The value of \((\vec A + \vec B) \times (\vec A - \vec B)\) is
1 \(0\)
2 \({A^2} - {B^2}\)
3 \(\vec B \times \vec A\)
4 \(2(\vec B \times \vec A)\)
Explanation:
\((\vec A + \vec B) \times (\vec A - \vec B) = \vec A \times \vec A - \vec A \times \vec B + \vec B \times \vec A - \vec B \times \vec B\) \( = 0 - \vec A \times \vec B + \vec B \times \vec A - 0\) \( = \vec B \times \vec A + \vec B \times \vec A = 2(\vec B \times \vec A)\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366225
The vectors from origin to the points A and B are \(\vec A = 3\hat i - 6\hat j + 2\hat k\) and \(\vec B = 2\hat i + \hat j - 2\hat k\) respectively. The area of the triangle \(OAB\) be
1 \(\frac{5}{2}\sqrt {17} \) sq.unit
2 \(\frac{2}{5}\sqrt {17} \) sq.unit
3 \(\frac{3}{5}\sqrt {17} \) sq.unit
4 \(\frac{5}{3}\sqrt {17} \) sq.unit
Explanation:
Given \(\overline {OA} = \vec a = 3\hat i - 6\hat j + 2\hat k\,\,{\rm{and}}\) \(\overline {OB} = \vec b = 2\hat i + \hat j - 2\hat k\) \(\therefore \;\;(\vec a \times \vec b) = \left| {\begin{array}{*{20}{c}}{\hat i}&{\hat j}&{\hat k}\\3&{ - 6}&2\\2&1&{ - 2}\end{array}} \right|\) \( = (12 - 2)\hat i + (4 + 6)\hat j + (3 + 12)\hat k\) \( = 10\hat i + 10\hat j + 15\hat k\) \( = \sqrt {425} = 5\sqrt {17} \) Area of \(\Delta \,OAB = \frac{1}{2}\left| {\vec a \times \vec b} \right| = \frac{{5\sqrt {17} }}{2}\) sq.unit.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366226
Two vectors \({\vec A}\) and \(\overrightarrow B \) making an angle \(\theta \) which one of the following relations is correct?
1 \(\vec A \times \vec B = \vec B \times \vec A\)
2 \(\vec A \times \vec B = AB\sin \theta \)
3 \(\vec A \times \vec B = AB\cos \theta \)
4 \(\vec A \times \vec B = - \vec B \times \vec A\)
Explanation:
Conceptual Question
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366227
\(\vec A\,\,{\rm{and}}\,\,\vec B\) are two vectors and \(\theta \) is the angle between them, if \(\left| {\vec A \times \vec B} \right| = \sqrt 3 (\vec A \cdot \vec B)\) the value of \(\theta \) is
366224
The value of \((\vec A + \vec B) \times (\vec A - \vec B)\) is
1 \(0\)
2 \({A^2} - {B^2}\)
3 \(\vec B \times \vec A\)
4 \(2(\vec B \times \vec A)\)
Explanation:
\((\vec A + \vec B) \times (\vec A - \vec B) = \vec A \times \vec A - \vec A \times \vec B + \vec B \times \vec A - \vec B \times \vec B\) \( = 0 - \vec A \times \vec B + \vec B \times \vec A - 0\) \( = \vec B \times \vec A + \vec B \times \vec A = 2(\vec B \times \vec A)\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366225
The vectors from origin to the points A and B are \(\vec A = 3\hat i - 6\hat j + 2\hat k\) and \(\vec B = 2\hat i + \hat j - 2\hat k\) respectively. The area of the triangle \(OAB\) be
1 \(\frac{5}{2}\sqrt {17} \) sq.unit
2 \(\frac{2}{5}\sqrt {17} \) sq.unit
3 \(\frac{3}{5}\sqrt {17} \) sq.unit
4 \(\frac{5}{3}\sqrt {17} \) sq.unit
Explanation:
Given \(\overline {OA} = \vec a = 3\hat i - 6\hat j + 2\hat k\,\,{\rm{and}}\) \(\overline {OB} = \vec b = 2\hat i + \hat j - 2\hat k\) \(\therefore \;\;(\vec a \times \vec b) = \left| {\begin{array}{*{20}{c}}{\hat i}&{\hat j}&{\hat k}\\3&{ - 6}&2\\2&1&{ - 2}\end{array}} \right|\) \( = (12 - 2)\hat i + (4 + 6)\hat j + (3 + 12)\hat k\) \( = 10\hat i + 10\hat j + 15\hat k\) \( = \sqrt {425} = 5\sqrt {17} \) Area of \(\Delta \,OAB = \frac{1}{2}\left| {\vec a \times \vec b} \right| = \frac{{5\sqrt {17} }}{2}\) sq.unit.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366226
Two vectors \({\vec A}\) and \(\overrightarrow B \) making an angle \(\theta \) which one of the following relations is correct?
1 \(\vec A \times \vec B = \vec B \times \vec A\)
2 \(\vec A \times \vec B = AB\sin \theta \)
3 \(\vec A \times \vec B = AB\cos \theta \)
4 \(\vec A \times \vec B = - \vec B \times \vec A\)
Explanation:
Conceptual Question
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
366227
\(\vec A\,\,{\rm{and}}\,\,\vec B\) are two vectors and \(\theta \) is the angle between them, if \(\left| {\vec A \times \vec B} \right| = \sqrt 3 (\vec A \cdot \vec B)\) the value of \(\theta \) is
