MCQ_SINGLE

If \(\vec{a} + \vec{b} + \vec{c} = \vec{0}\), \(|\vec{a}| = \sqrt{37}\), \(|\vec{b}| = 3\) and \(|\vec{c}| = 4\), then the angle between \(\vec{b}\) and \(\vec{c}\) is

SA

The scalar product of the vector $\vec{a}=\hat{i}-\hat{j}+2\hat{k}$ with a unit vector along sum of vectors $\vec{b}=2\hat{i}-4\hat{j}+5\hat{k}$ and $\vec{c}=\lambda\hat{i}-2\hat{j}-3\hat{k}$ is equal to 1. Find the value of $\lambda$.

VSA

If $\vec{r}=3\hat{i}-2\hat{j}+6\hat{k}$, find the value of $(\vec{r}\times\hat{j})\cdot(\vec{r}\times\hat{k})-12$

MCQ_SINGLE

If the sides AB and AC of \(\triangle ABC\) are represented by vectors \(\hat{j}+\hat{k}\) and \(3\hat{i}-\hat{j}+4\hat{k}\) respectively, then the length of the median through A on BC is:

VSA

If $\vec{a}$ and $\vec{b}$ are two non-collinear vectors, then find x, such that $\vec{\alpha}=(x-2)\vec{a}+\vec{b}$ and $\vec{\beta}=(3+2x)\vec{a}-2\vec{b}$ are collinear.

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