SA

Find the distance of the point $(-1, -5, -10)$ from the point of intersection of the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $\frac{x-4}{5}=\frac{y-1}{2}=z$.

SA

Find a point on the line $\frac{x-2}{3}=\frac{1-y}{2}=\frac{z-3}{2}$ at a distance of $\sqrt{2}$ units from the point (1, 2, 3).

MCQ_SINGLE

The equation of a line parallel to the vector \(3\hat{i}+\hat{j}+2\hat{k}\) and passing through the point \((4, -3, 7)\) is:

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 $\frac{\pi}{2}$ :

VSA

A man needs to hang two lanterns on a straight wire whose end points have coordinates $A(4,1,-2)$ and $B(6,2,-3)$. Find the coordinates of the points where he hangs the lanterns such that these points trisect the wire AB.

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