91Ó°ÊÓ

The vector that must be added to the vector \(\hat{i}-3 \hat{j}+2 \hat{k}\) and \(3 \hat{i}+6 \hat{j}-7 \hat{k}\) so that the resultant vector is a unit vector along the \(y\) -axis is (a) \(4 \hat{i}|2 \hat{j}| 5 \hat{k}\) (b) \(\quad 4 \hat{i} \quad 2 \hat{j} \mid 5 \hat{k}\) (c) \(3 \hat{i}|4 \hat{j}| 5 \hat{k}\) (d) null vector

If the angle between the vectors \(\vec{A}\) and \(\vec{B}\) is \(\theta\), the value of the product \((\vec{B} \times \vec{A}) \cdot \vec{A}\) is cqual to (a) \(B A^{2} \cos \theta\) (b) \(B A^{2} \sin \theta\) (c) \(B A^{2} \sin \theta \cos \theta\) (d) zero