SA

If $\vec{a}$ and $\vec{b}$ are unit vectors inclined with each other at an angle $\theta$, then prove that $\frac{1}{2}|\vec{a}-\vec{b}|=\sin\frac{\theta}{2}$.

SA

If $\vec{a}$, $\vec{b}$ and $\vec{c}$ are unit vectors, then prove that $|\vec{a}-\vec{b}|^{2}+|\vec{b}-\vec{c}|^{2}+|\vec{c}-\vec{a}|^{2}\le 9$.

MCQ_SINGLE

Vector of magnitude 3 making equal angles with x and y axes and perpendicular to z axis is

VSA

The diagonals of a parallelogram are given by $\vec{a}=2\hat{i}-\hat{j}+\hat{k}$ and $\vec{b}=\hat{i}+3\hat{j}-\hat{k}$. Find the area of the parallelogram.

MCQ_SINGLE

The value of $(\hat{i}\times\hat{j})\cdot \hat{j}+(\hat{j}\times\hat{i}) \hat{k}:$

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