Question

If v₁ = (3,-4) and v₂ = (2,6), then v₁v₂ is equal to which of the following?

O A. (-12,-24)
OB. 30
O C. -18
OD. (6,-24)

Answer 1

C. -18

Explanation:

Scalar Product (Dot Product) of two vectors

`\displaystyle \vec{a} \cdot \vec{b}=\sum_(i=1)^na_ib_i`

`\textsf{If }\: \vec{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k} \quad \textsf{and } \quad \vec{b}=b_1\hat{i}+b_2\hat{j}+b_3\hat{k}`

`\textsf{then }\quad \vec{a} \cdot \vec{b}=a_1b_1+a_2b_2+a_3b_3`

Given:

• v₁ = (3, -4)
• v₂ = (2, 6)

⇒ v₁ · v₂ = (3 · 2) + (-4 · 6)

⇒ v₁ · v₂ = 6 + (-24)

⇒ v₁ · v₂ = 6 - 24

⇒ v₁ · v₂ = -18