State whether the result is a vector or a scalar. (3w · v)u

Question

Use the vectors and to find the indicated quantity. State whether the result is a vector or a scalar.

(3w · v)u

Answer 1

Step 1 :

Definition of vector addition and scalar multiplication :

Let and be vectors and let k be a scalar.

Then the sum of u and v is the vector :

The scalar multiple of k times u is the vector :

Definition of the dot product :

The dot product of and  is

Step 2 :

The vectors are and

The expression is

Evaluation of :

 

Evaluation of :

Evaluation of :

Thus,

The value of and it is a vector.

Solution :

The value of and it is a vector.