VSA

If the lines $\frac{x-3}{1}=\frac{1-y}{1}=\frac{z+2}{p}$ and $\frac{2-x}{3}=\frac{y+1}{5}=\frac{z+56}{2p}$ are perpendicular to each other, then find the value(s) of p.

LA

Two vertices of the parallelogram ABCD are given as $A(-1,2,1)$ and $B(1,-2,5)$. If the equation of the line passing through C and D is $\frac{x-4}{1}=\frac{y+7}{-2}=\frac{z-8}{2}$ then find the distance between sides AB and CD. Hence, find the area of parallelogram ABCD.

LA

Find the image of the point (-1,5,2) in the line $\frac{2x-4}{2}=\frac{y}{2}=\frac{2-z}{3}$. Find the length of the line segment joining the points (given point and the image point).

MCQ_SINGLE

The value of $\lambda$ for which the angle between the lines $\vec{r}=\hat{i}+\hat{j}+\hat{k}+p(2\hat{i}+\hat{j}+2\hat{k})$ and $\vec{r}=(1+q)\hat{i}+(1+q\lambda)\hat{j}+(1+q)\hat{k}$ is $\frac{\pi}{2}$ :

LA

Find the value of p if the shortest distance between the lines $\vec{r}=(\hat{i}+2\hat{j}+\hat{k})+\lambda(\hat{i}-\hat{j}+\hat{k})$ and $\vec{r}=(p\hat{i}-\hat{j}-\hat{k})+\mu(2\hat{i}+\hat{j}+2\hat{k})$ is $\frac{3}{\sqrt{2}}$ units.

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