00. Scalar and Vector Quantities
Motion in Plane

143640 Let \(\left|\overrightarrow{\mathrm{A}}_{1}\right|=3,\left|\overrightarrow{\mathrm{A}}_{2}\right|=5\) and
\(\left|\vec{A}_{1}+\vec{A}_{2}\right|=5\). The value of
\(\left(\mathbf{2} \vec{A}_{1}+\mathbf{3} \vec{A}_{2}\right) \cdot\left(3 \vec{A}_{1}-\mathbf{2} \vec{A}_{2}\right)\) is

1 -106.5
2 -112.5
3 -99.5
4 -118.5
Motion in Plane

143641 In the cube of side ' \(a\) ' shown in the figure, the vector from the central point of the face \(A B O D\) to the central point of the face BEFO will be

1 \(\frac{1}{2} \mathrm{a}(\hat{\mathrm{i}}-\hat{\mathrm{k}})\)
2 \(\frac{1}{2} \mathrm{a}(\hat{\mathrm{j}}-\hat{\mathrm{i}})\)
3 \(\frac{1}{2} \mathrm{a}(\hat{\mathrm{j}}-\hat{\mathrm{k}})\)
4 \(\frac{1}{2} \mathrm{a}(\hat{\mathrm{k}}-\hat{\mathrm{i}})\)
Motion in Plane

143642 If \(\vec{A} \times \vec{B}=\vec{B} \times \vec{A}\), then the angle between \(A\) and \(B\) is

1 \(\pi\)
2 \(\pi / 3\)
3 \(\pi / 2\)
4 \(\pi / 4\)
Motion in Plane

143643 \(\vec{A}=3 \hat{i}+4 \hat{j}+2 \hat{k}, \vec{B}=6 \hat{i}-\hat{j}+3 \hat{k} \quad\) Find a vector parallel to \(\bar{A}\) whose magnitude equal to that of \(\overline{\mathbf{B}}\)

1 \(\sqrt{\frac{46}{29}}(3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
2 \(\sqrt{\frac{46}{29}}(6 \hat{\mathrm{i}}-\hat{\mathrm{j}}+3 \hat{\mathrm{k}})\)
3 \(\sqrt{\frac{29}{46}}(3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
4 \(\sqrt{\frac{29}{46}}(6 \hat{\mathrm{i}}-\hat{\mathrm{j}}+3 \hat{\mathrm{k}})\)
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Motion in Plane

143640 Let \(\left|\overrightarrow{\mathrm{A}}_{1}\right|=3,\left|\overrightarrow{\mathrm{A}}_{2}\right|=5\) and
\(\left|\vec{A}_{1}+\vec{A}_{2}\right|=5\). The value of
\(\left(\mathbf{2} \vec{A}_{1}+\mathbf{3} \vec{A}_{2}\right) \cdot\left(3 \vec{A}_{1}-\mathbf{2} \vec{A}_{2}\right)\) is

1 -106.5
2 -112.5
3 -99.5
4 -118.5
Motion in Plane

143641 In the cube of side ' \(a\) ' shown in the figure, the vector from the central point of the face \(A B O D\) to the central point of the face BEFO will be

1 \(\frac{1}{2} \mathrm{a}(\hat{\mathrm{i}}-\hat{\mathrm{k}})\)
2 \(\frac{1}{2} \mathrm{a}(\hat{\mathrm{j}}-\hat{\mathrm{i}})\)
3 \(\frac{1}{2} \mathrm{a}(\hat{\mathrm{j}}-\hat{\mathrm{k}})\)
4 \(\frac{1}{2} \mathrm{a}(\hat{\mathrm{k}}-\hat{\mathrm{i}})\)
Motion in Plane

143642 If \(\vec{A} \times \vec{B}=\vec{B} \times \vec{A}\), then the angle between \(A\) and \(B\) is

1 \(\pi\)
2 \(\pi / 3\)
3 \(\pi / 2\)
4 \(\pi / 4\)
Motion in Plane

143643 \(\vec{A}=3 \hat{i}+4 \hat{j}+2 \hat{k}, \vec{B}=6 \hat{i}-\hat{j}+3 \hat{k} \quad\) Find a vector parallel to \(\bar{A}\) whose magnitude equal to that of \(\overline{\mathbf{B}}\)

1 \(\sqrt{\frac{46}{29}}(3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
2 \(\sqrt{\frac{46}{29}}(6 \hat{\mathrm{i}}-\hat{\mathrm{j}}+3 \hat{\mathrm{k}})\)
3 \(\sqrt{\frac{29}{46}}(3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
4 \(\sqrt{\frac{29}{46}}(6 \hat{\mathrm{i}}-\hat{\mathrm{j}}+3 \hat{\mathrm{k}})\)
Motion in Plane

143640 Let \(\left|\overrightarrow{\mathrm{A}}_{1}\right|=3,\left|\overrightarrow{\mathrm{A}}_{2}\right|=5\) and
\(\left|\vec{A}_{1}+\vec{A}_{2}\right|=5\). The value of
\(\left(\mathbf{2} \vec{A}_{1}+\mathbf{3} \vec{A}_{2}\right) \cdot\left(3 \vec{A}_{1}-\mathbf{2} \vec{A}_{2}\right)\) is

1 -106.5
2 -112.5
3 -99.5
4 -118.5
Motion in Plane

143641 In the cube of side ' \(a\) ' shown in the figure, the vector from the central point of the face \(A B O D\) to the central point of the face BEFO will be

1 \(\frac{1}{2} \mathrm{a}(\hat{\mathrm{i}}-\hat{\mathrm{k}})\)
2 \(\frac{1}{2} \mathrm{a}(\hat{\mathrm{j}}-\hat{\mathrm{i}})\)
3 \(\frac{1}{2} \mathrm{a}(\hat{\mathrm{j}}-\hat{\mathrm{k}})\)
4 \(\frac{1}{2} \mathrm{a}(\hat{\mathrm{k}}-\hat{\mathrm{i}})\)
Motion in Plane

143642 If \(\vec{A} \times \vec{B}=\vec{B} \times \vec{A}\), then the angle between \(A\) and \(B\) is

1 \(\pi\)
2 \(\pi / 3\)
3 \(\pi / 2\)
4 \(\pi / 4\)
Motion in Plane

143643 \(\vec{A}=3 \hat{i}+4 \hat{j}+2 \hat{k}, \vec{B}=6 \hat{i}-\hat{j}+3 \hat{k} \quad\) Find a vector parallel to \(\bar{A}\) whose magnitude equal to that of \(\overline{\mathbf{B}}\)

1 \(\sqrt{\frac{46}{29}}(3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
2 \(\sqrt{\frac{46}{29}}(6 \hat{\mathrm{i}}-\hat{\mathrm{j}}+3 \hat{\mathrm{k}})\)
3 \(\sqrt{\frac{29}{46}}(3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
4 \(\sqrt{\frac{29}{46}}(6 \hat{\mathrm{i}}-\hat{\mathrm{j}}+3 \hat{\mathrm{k}})\)
Motion in Plane

143640 Let \(\left|\overrightarrow{\mathrm{A}}_{1}\right|=3,\left|\overrightarrow{\mathrm{A}}_{2}\right|=5\) and
\(\left|\vec{A}_{1}+\vec{A}_{2}\right|=5\). The value of
\(\left(\mathbf{2} \vec{A}_{1}+\mathbf{3} \vec{A}_{2}\right) \cdot\left(3 \vec{A}_{1}-\mathbf{2} \vec{A}_{2}\right)\) is

1 -106.5
2 -112.5
3 -99.5
4 -118.5
Motion in Plane

143641 In the cube of side ' \(a\) ' shown in the figure, the vector from the central point of the face \(A B O D\) to the central point of the face BEFO will be

1 \(\frac{1}{2} \mathrm{a}(\hat{\mathrm{i}}-\hat{\mathrm{k}})\)
2 \(\frac{1}{2} \mathrm{a}(\hat{\mathrm{j}}-\hat{\mathrm{i}})\)
3 \(\frac{1}{2} \mathrm{a}(\hat{\mathrm{j}}-\hat{\mathrm{k}})\)
4 \(\frac{1}{2} \mathrm{a}(\hat{\mathrm{k}}-\hat{\mathrm{i}})\)
Motion in Plane

143642 If \(\vec{A} \times \vec{B}=\vec{B} \times \vec{A}\), then the angle between \(A\) and \(B\) is

1 \(\pi\)
2 \(\pi / 3\)
3 \(\pi / 2\)
4 \(\pi / 4\)
Motion in Plane

143643 \(\vec{A}=3 \hat{i}+4 \hat{j}+2 \hat{k}, \vec{B}=6 \hat{i}-\hat{j}+3 \hat{k} \quad\) Find a vector parallel to \(\bar{A}\) whose magnitude equal to that of \(\overline{\mathbf{B}}\)

1 \(\sqrt{\frac{46}{29}}(3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
2 \(\sqrt{\frac{46}{29}}(6 \hat{\mathrm{i}}-\hat{\mathrm{j}}+3 \hat{\mathrm{k}})\)
3 \(\sqrt{\frac{29}{46}}(3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
4 \(\sqrt{\frac{29}{46}}(6 \hat{\mathrm{i}}-\hat{\mathrm{j}}+3 \hat{\mathrm{k}})\)
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here