Question

Find a ⋅ b.

a = 9i - 6j, b = 5i + 5j

a. -75
b. <45, -30>
c. <14, -1>
d. 15

Answer 1

a.b = 9.5 + (-6).5=15

Answer 2

The correct option is d. 15

Explanation:

Consider the provided information.

We need to find the a ⋅ b

The given vector is:

a = 9i - 6j, b = 5i + 5j

`\vec{a} = 9i - 6j \cdot \vec{b}= 5i + 5j`

Use the vector multiplication as shown:

`a = a_1, a_2,…, a_n\ \text{and}\ b = b_1, b_2,…, b_n` is defined as:

`a\cdot b =a_1b_1+a_2b_2...a_nb_n`

Now by using the above formula:

`\vec{a}=9i-6j\cdot \vec{b}= 5i + 5j=45-30=15`

Hence, the correct option is d. 15