# Vector $\vec{b}$ is obtained by rotating $\vec{a}=\hat{\imath}+\hat{\jmath}$ by $90^{\circ}$ about $\hat{k},$ where $\hat{\imath}, \hat{\jmath}$ and $\hat{k}$ are unit vectors along the $x, y$ and $z$ axes, respectively. $\vec{b}$ is given by (A) $\hat{\imath}-\hat{\jmath}$ (B) $-\hat{\imath}+\hat{\jmath}$ (C) $\hat{\imath}+\hat{\jmath}$ (D) $-\hat{\imath}-\hat{\jmath}$

## Question ID - 155432 :- Vector $\vec{b}$ is obtained by rotating $\vec{a}=\hat{\imath}+\hat{\jmath}$ by $90^{\circ}$ about $\hat{k},$ where $\hat{\imath}, \hat{\jmath}$ and $\hat{k}$ are unit vectors along the $x, y$ and $z$ axes, respectively. $\vec{b}$ is given by (A) $\hat{\imath}-\hat{\jmath}$ (B) $-\hat{\imath}+\hat{\jmath}$ (C) $\hat{\imath}+\hat{\jmath}$ (D) $-\hat{\imath}-\hat{\jmath}$

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(B) $-\hat{\imath}+\hat{\jmath}$

Next Question :

A scalar function is given by $f(x, y)=x^{2}+y^{2}$. Take $\hat{\imath}$ and $\hat{\jmath}$ as unit vectors along the $x$ and $y$ axes, respectively. At $(x, y)=(3,4),$ the direction along which $f$ increases the fastest is
(A) $\frac{1}{5}(4 \hat{\imath}-3 \hat{\jmath})$
(B) $\frac{1}{5}(3 \hat{\imath}-4 \hat{\jmath})$
(C) $\frac{1}{5}(3 \hat{\imath}+4 \hat{\jmath})$
(D) $\frac{1}{5}(4 \hat{\imath}+3 \hat{\jmath})$ 