Question

If the points (-1,-1,2), (2,m,5) and (3,11,6) are collinear, then find the value of m.

• A. 6
• B. 8
• C. 10
• D. 12

Answer 1

The correct option is B 8

Let the given points be $A(-1,-1,2),B(2,m,5),C(3,11,6)$.

Then, $\overrightarrow{AB}=(2+1)\hat{i}+(m+1)\hat{j}+(5-2)\hat{k}$

$=3\hat{i}+(m+1)\hat{j}+3\hat{k}$

and, $\overrightarrow{AC}=(3+1)\hat{i}+(11+1)\hat{j}+(6-2)\hat{k}$

$=4\hat{i}+12\hat{j}+4\hat{k}$

Now, if A, B and C are collinear, then $\overrightarrow{AB}=\lambda \overrightarrow{AC}$

$3\hat{i}+(m+1)\hat{j}+3\hat{k}=\lambda (4\hat{i}+12\hat{j}+4\hat{k})$

On comparing, $3=4\lambda$

$\lambda =\frac{3}{4}$

And, $m+1=12\lambda$

$m=1=9$

$m=8$