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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366233 Which of the following is the unit vector perpendicular to \({\vec A}\) and \({\vec B}\) ?

1 \(\frac{{\hat A \times \hat B}}{{AB\sin \theta }}\)

2 \(\frac{{\hat A \times \hat B}}{{AB\cos \theta }}\)

3 \(\frac{{\vec A \times \vec B}}{{AB\sin \theta }}\)

4 \(\frac{{\vec A \times \vec B}}{{AB\cos \theta }}\)

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366234 What is the unit vector perpendicular to the following vectors \(2\hat i + 2\hat j - \hat k\) and \(6\hat i - 3\hat j + 2\hat k\) ?

1 \(\frac{{\hat i + 10\hat j - 18\hat k}}{{5\sqrt {17} }}\)

2 \(\frac{{\hat i - 10\hat j + 18\hat k}}{{5\sqrt {17} }}\)

3 \(\frac{{\hat i - 10\hat j - 18\hat k}}{{5\sqrt {17} }}\)

4 \(\frac{{\hat i + 10\hat j + 18\hat k}}{{5\sqrt {17} }}\)

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366235 If \(\left| {\vec A \times \vec B} \right| = \sqrt 3 \;\vec A \cdot \vec B\), then the value of \(\left| {\vec A + \vec B} \right|\) is

1 \({\left( {{A^2} + {B^2} + \frac{{AB}}{{\sqrt 3 }}} \right)^{1/2}}\)

2 \(A + B\)

3 \({({A^2} + {B^2} + \sqrt 3 AB)^{1/2}}\)

4 \({({A^2} + {B^2} + AB)^{1/2}}\)

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366236 If the vectors \(\overrightarrow A = 2\hat i + 4\hat j\) and \(\overrightarrow B = 5\hat i - p\hat j\) are parallel to each other, the magnitude of B is

1 \(5\sqrt 5 \)

2 \( - 10\)

3 \(15\)

4 \( - 4\,\hat i\)

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366233 Which of the following is the unit vector perpendicular to \({\vec A}\) and \({\vec B}\) ?

1 \(\frac{{\hat A \times \hat B}}{{AB\sin \theta }}\)

2 \(\frac{{\hat A \times \hat B}}{{AB\cos \theta }}\)

3 \(\frac{{\vec A \times \vec B}}{{AB\sin \theta }}\)

4 \(\frac{{\vec A \times \vec B}}{{AB\cos \theta }}\)

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366234 What is the unit vector perpendicular to the following vectors \(2\hat i + 2\hat j - \hat k\) and \(6\hat i - 3\hat j + 2\hat k\) ?

1 \(\frac{{\hat i + 10\hat j - 18\hat k}}{{5\sqrt {17} }}\)

2 \(\frac{{\hat i - 10\hat j + 18\hat k}}{{5\sqrt {17} }}\)

3 \(\frac{{\hat i - 10\hat j - 18\hat k}}{{5\sqrt {17} }}\)

4 \(\frac{{\hat i + 10\hat j + 18\hat k}}{{5\sqrt {17} }}\)

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366235 If \(\left| {\vec A \times \vec B} \right| = \sqrt 3 \;\vec A \cdot \vec B\), then the value of \(\left| {\vec A + \vec B} \right|\) is

1 \({\left( {{A^2} + {B^2} + \frac{{AB}}{{\sqrt 3 }}} \right)^{1/2}}\)

2 \(A + B\)

3 \({({A^2} + {B^2} + \sqrt 3 AB)^{1/2}}\)

4 \({({A^2} + {B^2} + AB)^{1/2}}\)

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366236 If the vectors \(\overrightarrow A = 2\hat i + 4\hat j\) and \(\overrightarrow B = 5\hat i - p\hat j\) are parallel to each other, the magnitude of B is

1 \(5\sqrt 5 \)

2 \( - 10\)

3 \(15\)

4 \( - 4\,\hat i\)

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366233 Which of the following is the unit vector perpendicular to \({\vec A}\) and \({\vec B}\) ?

1 \(\frac{{\hat A \times \hat B}}{{AB\sin \theta }}\)

2 \(\frac{{\hat A \times \hat B}}{{AB\cos \theta }}\)

3 \(\frac{{\vec A \times \vec B}}{{AB\sin \theta }}\)

4 \(\frac{{\vec A \times \vec B}}{{AB\cos \theta }}\)

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366234 What is the unit vector perpendicular to the following vectors \(2\hat i + 2\hat j - \hat k\) and \(6\hat i - 3\hat j + 2\hat k\) ?

1 \(\frac{{\hat i + 10\hat j - 18\hat k}}{{5\sqrt {17} }}\)

2 \(\frac{{\hat i - 10\hat j + 18\hat k}}{{5\sqrt {17} }}\)

3 \(\frac{{\hat i - 10\hat j - 18\hat k}}{{5\sqrt {17} }}\)

4 \(\frac{{\hat i + 10\hat j + 18\hat k}}{{5\sqrt {17} }}\)

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366235 If \(\left| {\vec A \times \vec B} \right| = \sqrt 3 \;\vec A \cdot \vec B\), then the value of \(\left| {\vec A + \vec B} \right|\) is

1 \({\left( {{A^2} + {B^2} + \frac{{AB}}{{\sqrt 3 }}} \right)^{1/2}}\)

2 \(A + B\)

3 \({({A^2} + {B^2} + \sqrt 3 AB)^{1/2}}\)

4 \({({A^2} + {B^2} + AB)^{1/2}}\)

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366236 If the vectors \(\overrightarrow A = 2\hat i + 4\hat j\) and \(\overrightarrow B = 5\hat i - p\hat j\) are parallel to each other, the magnitude of B is

1 \(5\sqrt 5 \)

2 \( - 10\)

3 \(15\)

4 \( - 4\,\hat i\)

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366233 Which of the following is the unit vector perpendicular to \({\vec A}\) and \({\vec B}\) ?

1 \(\frac{{\hat A \times \hat B}}{{AB\sin \theta }}\)

2 \(\frac{{\hat A \times \hat B}}{{AB\cos \theta }}\)

3 \(\frac{{\vec A \times \vec B}}{{AB\sin \theta }}\)

4 \(\frac{{\vec A \times \vec B}}{{AB\cos \theta }}\)

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366234 What is the unit vector perpendicular to the following vectors \(2\hat i + 2\hat j - \hat k\) and \(6\hat i - 3\hat j + 2\hat k\) ?

1 \(\frac{{\hat i + 10\hat j - 18\hat k}}{{5\sqrt {17} }}\)

2 \(\frac{{\hat i - 10\hat j + 18\hat k}}{{5\sqrt {17} }}\)

3 \(\frac{{\hat i - 10\hat j - 18\hat k}}{{5\sqrt {17} }}\)

4 \(\frac{{\hat i + 10\hat j + 18\hat k}}{{5\sqrt {17} }}\)

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366235 If \(\left| {\vec A \times \vec B} \right| = \sqrt 3 \;\vec A \cdot \vec B\), then the value of \(\left| {\vec A + \vec B} \right|\) is

1 \({\left( {{A^2} + {B^2} + \frac{{AB}}{{\sqrt 3 }}} \right)^{1/2}}\)

2 \(A + B\)

3 \({({A^2} + {B^2} + \sqrt 3 AB)^{1/2}}\)

4 \({({A^2} + {B^2} + AB)^{1/2}}\)

PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

366236 If the vectors \(\overrightarrow A = 2\hat i + 4\hat j\) and \(\overrightarrow B = 5\hat i - p\hat j\) are parallel to each other, the magnitude of B is

1 \(5\sqrt 5 \)

2 \( - 10\)

3 \(15\)

4 \( - 4\,\hat i\)

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