If two vectors P → = i ^ + 2 m j ^ + m k ^ and Q → = 4 i ^ - 2 j ^ + m k ^ are perpendicular to each other. Then, the value of m will be

Step-by-step solution

For two vectors to be perpendicular, their dot product is equal to zero. So, P → · Q → = 0 ⇒ i ^ + 2 m j ^ + m k ^ · 4 i ^ - 2 j ^ + m k ^ = 0 ⇒ 4 - 4 m + m 2 = 0 ⇒ m - 2 2 = 0 ⇒ m = 2