Question

If points $\hat{i}+\hat{j},\hat{i}-\hat{j}$ and $p\hat{i}+q\hat{j}+r\hat{k}$ are collinear, then

• A. $p=1$
• B. $r=0$
• C. $q\in R$
• D. $q\ne 1$

Answer 1

Answer: (A), (B), (D)

The correct options are
A $r=0$
B $p=1$
D $q\ne 1$

Points $A(\hat{i}+\hat{j}),B(\hat{i}-\hat{j})$ and $C(p\hat{i}+q\hat{j}+r\hat{k})$ are collinear
Now $\overrightarrow{AB}=-2\hat{j}$ and $\overrightarrow{BC}=(p-1)\hat{i}+(q-1)\hat{j}+rk$
Vectors $\overrightarrow{AB}$ and $\overrightarrow{BC}$ must be collinear
$\Rightarrow p=1,r=0$ and $q\ne 1$