For what value of m, the vector E=3i+mj-2k and . . .

Question : For what value of m, the vector E=3i+mj-2k and vector B=mi+7j+5k are orthogonal?

Doubt by Suhani

Solution :

Please Note that here the word orthogonal means perpendicular and we know if two vectors are perpendicular then their dot product (Scalar Product) is equal to zero.

E=3i+mj-2k

B=mi+7j+5k

E and B are orthogonal vector

Hence, E.B = 0
(3i+mj-2k)(mi+7j+5k) = 0
(3)(m)+(m)(7)+(-2)(5)=0
3m+7m-10=0
10m-10=0
10m=10
m=10/10
m=1

Hence, the required value of m is 1.