Menu Close

if-the-point-A-B-C-with-position-vector-20i-j-5i-j-and-10i-13j-are-collinear-then-the-value-of-is-

Tinku Tara 0 Comments
Pin




Question Number 62241 by vishnurajput8081@gmail.com last updated on 18/Jun/19
if the point A B C with position vector (20i^� +λj^� ) (5i^� −j^� ) and(10i^� −13j^� ) are collinear then the value of λ is:
ifthepointABCwithpositionvector(20i^+λj^)(5i^−j^)and(10i^−13j^)arecollinearthenthevalueofλis:
Answered by tanmay last updated on 18/Jun/19
AB^→ =OB^→ −OA^→ =i(5−20)+j(−1−λ)=i(−15)+j(−1−λ) BC^→ =OC^→ −OB^→ =i(10−5)+j(−13+1)=i(5)+j(−12) AB^→ ×BC^→ =0 [(−15)i+j(−1−λ)]×[5i−12j]=0 −75(i×i)+180(i×j)+(−5−5λ)(j×i)+(12+12λ)(j×j)=0 (i×j)(180+5+5λ)=0 5λ+185=0 λ=−37
AB→=OB→−OA→=i(5−20)+j(−1−λ)=i(−15)+j(−1−λ)BC→=OC→−OB→=i(10−5)+j(−13+1)=i(5)+j(−12)AB→×BC→=0[(−15)i+j(−1−λ)]×[5i−12j]=0−75(i×i)+180(i×j)+(−5−5λ)(j×i)+(12+12λ)(j×j)=0(i×j)(180+5+5λ)=05λ+185=0λ=−37

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *