MCQ_SINGLE

If vectors $\vec{a}=3\hat{i}+2\hat{j}+\lambda\hat{k}$ and $\vec{b}=2\hat{i}-4\hat{j}+5\hat{k}$, represent the two strips of the Red Cross sign placed outside a doctor's clinic, then the value of $\lambda$ is :

MCQ_SINGLE

If position vector $\vec{p}$ of a point (24, n) is such that $|\vec{p}|=25$, then the value of n is:

VSA

If the position vectors of three points A, B and C are $3\hat{i}+\hat{j}$, $5\hat{i}+6\hat{j}-3\hat{k}$ and $4\hat{j}$ respectively, then show that they form an isosceles triangle.

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

Let three toys A, B and C be placed in the same straight line. If the position vectors of A, B and C are $5\hat{i}-2\hat{j}$, $5\hat{i}+8\hat{j}$ and $a\hat{i}-52\hat{j}$ respectively, find the value of 'a'.

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