Let A, B , C be distinct points with position vectors i + j, , i … - Vidyadip

MCQ

Let $A, B , C$ be distinct points with position vectors $\hat i + \hat j,\,\hat i - \hat j,\,p\hat i - q\hat j + r\hat k$ respectively. Points $A, B , C$ are collinear, then which of the following can be correct

A
$p=q=r=1$
B
$p=q=r=0$
C
$p=q=2,r=0$
✓
$p=1,q=2,r=0$

✓

Answer

Correct option: D.

$p=1,q=2,r=0$

d
${\overrightarrow {AB} = - 2\hat i}$

${\overrightarrow {AC} = (p - 1)\hat i - (9 + 1)}$

${\hat j + \hat k = - (1 + 1)\hat j}$

$\begin{array}{*{20}{c}}
{\overrightarrow {AC} = \lambda \overrightarrow {AB} }&{p = 1}\\
{p - 1 = 0}&{q = 2\lambda - 1}\\
{( - q + 1) = 2\lambda :e = 0}&{r = 0}
\end{array}$

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