Question

Review the following information about vectors q and r.

q = ⟨–4, 1⟩

r = ⟨a, 3⟩

7(q + r) = ⟨–35, 28⟩

What is the value of a?

–31
–7
–5
–1

Answer 1

Answer:

D) -1

Step-by-step explanation:

got it right on edge :)

Answer 2

Vector addition is done by addition of the components

The value of a is -1

a = –1

Reason:

The given parameters are;

q = <-4, 1>

r = <a, 3>

7·(q + r) = <-35, 28>

Required:

The value of a

Solution;

By vector addition of the components of q, and r, we have;

• q + r = <-4 + a, 1 + 3> = <-4 + a, 4>

q + r =  <(-4 + a),    4>

By plugging in the value of q + r from the above step, we have;

• 7·(q + r) = <7 ×(-4 + a), 7 × 4> distribution property

7·(q + r)  = <-35, 28> Given

Therefore, by comparison of components, we have;

7 ×(-4 + a) = -35

• $-4 + a = -\dfrac{35}{7} = -5$

a = -5 + 4 = -1

a = –1

The correct option for the value of a is –1

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