Question

If u-ai + bj and v-ci + dj are vectors, then which of the following statements is not true?

A. The dot product of u and v is the same as the inner product of u and v.

B. The dot product of u and v is a scalar

C. The dot product of u and v is a vector.

D. The dot product of u and v is given by the expression ac+bd

Answer 1

Option C

Explanation:

Given that u-ai + bj and v-ci + dj are vectors

We have dot product

`u.v = (ai+bj).(ci+dj)` hence inner product of u and v. So option a is true

The dot product of u and v is a scalar is true because dot product is always a scalar

The dot product of u and v is a vector. is false because dot product is only a scalar and has no direction and hence cannot be a vector

The dot product of u and v is given by the expression ac+bd

True because we multiply corresponding i components and j components and add.

So only C is not true.