if the point A B C with position vector (20i^� +λj^� ) (5i^� −j^� ) and(10i^� −13j^� ) are collinear then the value of λ is:


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Question Number 62241 by vishnurajput8081@gmail.com last updated on 18/Jun/19

$i f t h e p o i n t A B C w i t h p o s i t i o n v e c t o r$ $(20 \hat{i} + λ \hat{j}) (5 \hat{i} - \hat{j}) a n d (10 \hat{i} - 13 \hat{j}) a r e$ $c o l l i n e a r t h e n t h e v a l u e o f λ i s :$
	Answered by tanmay last updated on 18/Jun/19

	$A \vec{B} = O \vec{B} - O \vec{A} = i (5 - 20) + j (- 1 - λ) = i (- 15) + j (- 1 - λ)$ $B \vec{C} = O \vec{C} - O \vec{B} = i (10 - 5) + j (- 13 + 1) = i (5) + j (- 12)$ $A \vec{B} \times B \vec{C} = 0$ $[(- 15) i + j (- 1 - λ)] \times [5 i - 12 j] = 0$ $- 75 (i \times i) + 180 (i \times j) + (- 5 - 5 λ) (j \times i) + (12 + 12 λ) (j \times j) = 0$ $(i \times j) (180 + 5 + 5 λ) = 0$ $5 λ + 185 = 0$ $λ = - 37$
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