Question

If either vector , then . But the converse need not be true. Justify your answer with an example.

Answer 1

Given, if either a → =0 or b → =0 then a → ⋅ b → =0.

Assume, a → =( i ^ + j ^ + k ^ ) and b → =( i ^ −2 j ^ + k ^ ).

Dot product of vectors is,

a → ⋅ b → =( i ^ + j ^ + k ^ )⋅( i ^ −2 j ^ + k ^ ) =1⋅1+1⋅( −2 )+1⋅1 =0

Here, a → ⋅ b → =0. But, a → ≠0 and b → ≠0.

Thus, the converse of the statement need not be true.