143524
If \(\vec{A}, \vec{B}\) are perpendicular vectors \(\overrightarrow{\mathrm{A}}=5 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}\) \(\overrightarrow{\mathrm{B}}=2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\mathbf{c} \hat{\mathbf{k}}\) The value of \(c\) is
143525
The resultant of the vectors \(A\) and \(B\) depends also on the angle \(\theta\) between them. The magnitude of the resultant is always given by
143526
\(\quad \overrightarrow{\mathbf{A}}\) and \(\overrightarrow{\mathbf{B}}\) are vectors such that \(|\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}|=\) \(|\vec{A}-\vec{B}|\). Then, the angle between them is
143527
When two vectors \(\vec{A}\) and \(\vec{B}\) of magnitude a and \(b\) are added, the magnitude of the resultant vector is always
1 equal to \((a+b)\)
2 less than \((a+b)\)
3 greater than \((\mathrm{a}+\mathrm{b})\)
4 not greater than \((\mathrm{a}+\mathrm{b})\)
Explanation:
D Given, \(|\overrightarrow{\mathrm{A}}|=\mathrm{a},|\overrightarrow{\mathrm{B}}|=\mathrm{b}\) \(|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|=\sqrt{\mathrm{a}^{2}+\mathrm{b}^{2}+2 \mathrm{ab} \cos \theta}\) \(|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|_{\max }=\sqrt{\mathrm{a}^{2}+\mathrm{b}^{2}+2 \mathrm{ab}} \quad[\text { For max, } \theta=0]\) \(|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|_{\max }=(\mathrm{a}+\mathrm{b})\) Hence, magnitude of resultant vector is not greater than \((\mathrm{a}+\mathrm{b})\)
EAMCET-1993
Motion in Plane
143529
The angle made by the vector \(\overrightarrow{\mathbf{A}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}\) with \(\mathbf{x}\) axis is
1 \(90^{\circ}\)
2 \(45^{\circ}\)
3 \(22.5^{\circ}\)
4 \(30^{\circ}\)
Explanation:
B Given that, \(\vec{A}=\hat{i}+\hat{j}\) \(|\vec{A}|=\sqrt{1^{2}+1^{2}}=\sqrt{2}\) \(A_{x}=1, A_{y}=1\) If \(\theta\) is the angle made by the vector with \(\mathrm{x}\)-axis than, \(\cos \theta=\frac{A_{x}}{|\vec{A}|} \Rightarrow \cos \theta=\frac{1}{\sqrt{2}}\) \(\theta=45^{\circ}\)
143524
If \(\vec{A}, \vec{B}\) are perpendicular vectors \(\overrightarrow{\mathrm{A}}=5 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}\) \(\overrightarrow{\mathrm{B}}=2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\mathbf{c} \hat{\mathbf{k}}\) The value of \(c\) is
143525
The resultant of the vectors \(A\) and \(B\) depends also on the angle \(\theta\) between them. The magnitude of the resultant is always given by
143526
\(\quad \overrightarrow{\mathbf{A}}\) and \(\overrightarrow{\mathbf{B}}\) are vectors such that \(|\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}|=\) \(|\vec{A}-\vec{B}|\). Then, the angle between them is
143527
When two vectors \(\vec{A}\) and \(\vec{B}\) of magnitude a and \(b\) are added, the magnitude of the resultant vector is always
1 equal to \((a+b)\)
2 less than \((a+b)\)
3 greater than \((\mathrm{a}+\mathrm{b})\)
4 not greater than \((\mathrm{a}+\mathrm{b})\)
Explanation:
D Given, \(|\overrightarrow{\mathrm{A}}|=\mathrm{a},|\overrightarrow{\mathrm{B}}|=\mathrm{b}\) \(|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|=\sqrt{\mathrm{a}^{2}+\mathrm{b}^{2}+2 \mathrm{ab} \cos \theta}\) \(|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|_{\max }=\sqrt{\mathrm{a}^{2}+\mathrm{b}^{2}+2 \mathrm{ab}} \quad[\text { For max, } \theta=0]\) \(|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|_{\max }=(\mathrm{a}+\mathrm{b})\) Hence, magnitude of resultant vector is not greater than \((\mathrm{a}+\mathrm{b})\)
EAMCET-1993
Motion in Plane
143529
The angle made by the vector \(\overrightarrow{\mathbf{A}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}\) with \(\mathbf{x}\) axis is
1 \(90^{\circ}\)
2 \(45^{\circ}\)
3 \(22.5^{\circ}\)
4 \(30^{\circ}\)
Explanation:
B Given that, \(\vec{A}=\hat{i}+\hat{j}\) \(|\vec{A}|=\sqrt{1^{2}+1^{2}}=\sqrt{2}\) \(A_{x}=1, A_{y}=1\) If \(\theta\) is the angle made by the vector with \(\mathrm{x}\)-axis than, \(\cos \theta=\frac{A_{x}}{|\vec{A}|} \Rightarrow \cos \theta=\frac{1}{\sqrt{2}}\) \(\theta=45^{\circ}\)
143524
If \(\vec{A}, \vec{B}\) are perpendicular vectors \(\overrightarrow{\mathrm{A}}=5 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}\) \(\overrightarrow{\mathrm{B}}=2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\mathbf{c} \hat{\mathbf{k}}\) The value of \(c\) is
143525
The resultant of the vectors \(A\) and \(B\) depends also on the angle \(\theta\) between them. The magnitude of the resultant is always given by
143526
\(\quad \overrightarrow{\mathbf{A}}\) and \(\overrightarrow{\mathbf{B}}\) are vectors such that \(|\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}|=\) \(|\vec{A}-\vec{B}|\). Then, the angle between them is
143527
When two vectors \(\vec{A}\) and \(\vec{B}\) of magnitude a and \(b\) are added, the magnitude of the resultant vector is always
1 equal to \((a+b)\)
2 less than \((a+b)\)
3 greater than \((\mathrm{a}+\mathrm{b})\)
4 not greater than \((\mathrm{a}+\mathrm{b})\)
Explanation:
D Given, \(|\overrightarrow{\mathrm{A}}|=\mathrm{a},|\overrightarrow{\mathrm{B}}|=\mathrm{b}\) \(|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|=\sqrt{\mathrm{a}^{2}+\mathrm{b}^{2}+2 \mathrm{ab} \cos \theta}\) \(|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|_{\max }=\sqrt{\mathrm{a}^{2}+\mathrm{b}^{2}+2 \mathrm{ab}} \quad[\text { For max, } \theta=0]\) \(|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|_{\max }=(\mathrm{a}+\mathrm{b})\) Hence, magnitude of resultant vector is not greater than \((\mathrm{a}+\mathrm{b})\)
EAMCET-1993
Motion in Plane
143529
The angle made by the vector \(\overrightarrow{\mathbf{A}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}\) with \(\mathbf{x}\) axis is
1 \(90^{\circ}\)
2 \(45^{\circ}\)
3 \(22.5^{\circ}\)
4 \(30^{\circ}\)
Explanation:
B Given that, \(\vec{A}=\hat{i}+\hat{j}\) \(|\vec{A}|=\sqrt{1^{2}+1^{2}}=\sqrt{2}\) \(A_{x}=1, A_{y}=1\) If \(\theta\) is the angle made by the vector with \(\mathrm{x}\)-axis than, \(\cos \theta=\frac{A_{x}}{|\vec{A}|} \Rightarrow \cos \theta=\frac{1}{\sqrt{2}}\) \(\theta=45^{\circ}\)
143524
If \(\vec{A}, \vec{B}\) are perpendicular vectors \(\overrightarrow{\mathrm{A}}=5 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}\) \(\overrightarrow{\mathrm{B}}=2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\mathbf{c} \hat{\mathbf{k}}\) The value of \(c\) is
143525
The resultant of the vectors \(A\) and \(B\) depends also on the angle \(\theta\) between them. The magnitude of the resultant is always given by
143526
\(\quad \overrightarrow{\mathbf{A}}\) and \(\overrightarrow{\mathbf{B}}\) are vectors such that \(|\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}|=\) \(|\vec{A}-\vec{B}|\). Then, the angle between them is
143527
When two vectors \(\vec{A}\) and \(\vec{B}\) of magnitude a and \(b\) are added, the magnitude of the resultant vector is always
1 equal to \((a+b)\)
2 less than \((a+b)\)
3 greater than \((\mathrm{a}+\mathrm{b})\)
4 not greater than \((\mathrm{a}+\mathrm{b})\)
Explanation:
D Given, \(|\overrightarrow{\mathrm{A}}|=\mathrm{a},|\overrightarrow{\mathrm{B}}|=\mathrm{b}\) \(|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|=\sqrt{\mathrm{a}^{2}+\mathrm{b}^{2}+2 \mathrm{ab} \cos \theta}\) \(|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|_{\max }=\sqrt{\mathrm{a}^{2}+\mathrm{b}^{2}+2 \mathrm{ab}} \quad[\text { For max, } \theta=0]\) \(|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|_{\max }=(\mathrm{a}+\mathrm{b})\) Hence, magnitude of resultant vector is not greater than \((\mathrm{a}+\mathrm{b})\)
EAMCET-1993
Motion in Plane
143529
The angle made by the vector \(\overrightarrow{\mathbf{A}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}\) with \(\mathbf{x}\) axis is
1 \(90^{\circ}\)
2 \(45^{\circ}\)
3 \(22.5^{\circ}\)
4 \(30^{\circ}\)
Explanation:
B Given that, \(\vec{A}=\hat{i}+\hat{j}\) \(|\vec{A}|=\sqrt{1^{2}+1^{2}}=\sqrt{2}\) \(A_{x}=1, A_{y}=1\) If \(\theta\) is the angle made by the vector with \(\mathrm{x}\)-axis than, \(\cos \theta=\frac{A_{x}}{|\vec{A}|} \Rightarrow \cos \theta=\frac{1}{\sqrt{2}}\) \(\theta=45^{\circ}\)
143524
If \(\vec{A}, \vec{B}\) are perpendicular vectors \(\overrightarrow{\mathrm{A}}=5 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}\) \(\overrightarrow{\mathrm{B}}=2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\mathbf{c} \hat{\mathbf{k}}\) The value of \(c\) is
143525
The resultant of the vectors \(A\) and \(B\) depends also on the angle \(\theta\) between them. The magnitude of the resultant is always given by
143526
\(\quad \overrightarrow{\mathbf{A}}\) and \(\overrightarrow{\mathbf{B}}\) are vectors such that \(|\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}|=\) \(|\vec{A}-\vec{B}|\). Then, the angle between them is
143527
When two vectors \(\vec{A}\) and \(\vec{B}\) of magnitude a and \(b\) are added, the magnitude of the resultant vector is always
1 equal to \((a+b)\)
2 less than \((a+b)\)
3 greater than \((\mathrm{a}+\mathrm{b})\)
4 not greater than \((\mathrm{a}+\mathrm{b})\)
Explanation:
D Given, \(|\overrightarrow{\mathrm{A}}|=\mathrm{a},|\overrightarrow{\mathrm{B}}|=\mathrm{b}\) \(|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|=\sqrt{\mathrm{a}^{2}+\mathrm{b}^{2}+2 \mathrm{ab} \cos \theta}\) \(|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|_{\max }=\sqrt{\mathrm{a}^{2}+\mathrm{b}^{2}+2 \mathrm{ab}} \quad[\text { For max, } \theta=0]\) \(|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|_{\max }=(\mathrm{a}+\mathrm{b})\) Hence, magnitude of resultant vector is not greater than \((\mathrm{a}+\mathrm{b})\)
EAMCET-1993
Motion in Plane
143529
The angle made by the vector \(\overrightarrow{\mathbf{A}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}\) with \(\mathbf{x}\) axis is
1 \(90^{\circ}\)
2 \(45^{\circ}\)
3 \(22.5^{\circ}\)
4 \(30^{\circ}\)
Explanation:
B Given that, \(\vec{A}=\hat{i}+\hat{j}\) \(|\vec{A}|=\sqrt{1^{2}+1^{2}}=\sqrt{2}\) \(A_{x}=1, A_{y}=1\) If \(\theta\) is the angle made by the vector with \(\mathrm{x}\)-axis than, \(\cos \theta=\frac{A_{x}}{|\vec{A}|} \Rightarrow \cos \theta=\frac{1}{\sqrt{2}}\) \(\theta=45^{\circ}\)
