Vectors 1 Question 17
18. The points with position vectors $60 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}, 40 \hat{\mathbf{i}}-8 \hat{\mathbf{j}}, a \hat{\mathbf{i}}-52 \hat{\mathbf{j}}$ are collinear, if
(1983, 1M)
(a) $a=-40$
(b) $a=40$
(c) $a=20$
(d) None of these
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Answer:
Correct Answer: 18. $c \in\left(-\frac{4}{3}, 0\right)$
Solution:
- Three points $A, B, C$ are collinear, if $\overrightarrow{\mathbf{A B}}=-20 \hat{\mathbf{i}}-11 \hat{\mathbf{j}}$ and $\overrightarrow{\mathbf{A C}}=(a-60) \hat{\mathbf{i}}-55 \hat{\mathbf{j}}$, then $\overrightarrow{\mathbf{A B}} | \overrightarrow{\mathbf{A C}}$
$\Rightarrow \frac{a-60}{-20}=\frac{-55}{-11} \Rightarrow a=-40$
