Question
Mathematics Question on Circle
Find the value of m for which the line r→=(i^+2k^)+λ(2i^−mj^−3k^) is parallel to the plane r→⋅(mi^+3j^+k^)=4 ?
A
(A) 2
B
(B) -2
C
(C) 3
D
(D) -3
Answer
(D) -3
Explanation
Solution
Explanation:
Given: Equation of line r→=(i^+2k^)+λ(2i^−mj^−3k^) and equation of plane r→⋅(mi^+3j^+k^)=4It is given that the given line is parallel to the given plane,As we know that, if the line r→=a→+λb→ is parallel to the plane r→⋅n→=q then b→⋅n→=0Here, b→=2i^−mj^−3k^ and n→=mi^+3j^+k^ ⇒b→⋅n→=2m−3m−3=0 ⇒m=−3Hence, the correct option is (D).