Question

The three points whose position vectors are $\overline{i}+2\overline{j}+3\overline{k,}$ $3\overline{i}+4\overline{j}+7\overline{k,}$ and $-3\overline{i}-2\overline{j}-5\overline{k}$

• A. Form the vertices of an equilateral triangle
• B. Form the vertices of an right angled triangle
• C. Are collinear
• D. Form the vertices of an isosceles triangle

Answer 1

Answer: (C)

Are collinear

$\overrightarrow{a}=\hat{i}+2\hat{j}+3\hat{k}$
$\overrightarrow{b}=3\hat{i}+4\hat{j}+7\hat{k}$
$\overrightarrow{c}=3\hat{i}-2\hat{j}-5\hat{k}$
$\overrightarrow{ca}=4\hat{i}+4\hat{j}+8\hat{k}$
$\overrightarrow{cb}=6\hat{i}+6\hat{j}+12\hat{k}$
$\overrightarrow{cb}=\frac{3}{2}\left(\overrightarrow{ca}\right)$
So, $\overrightarrow{a},\overrightarrow{c},\overrightarrow{b}$ are collinear.