The Dot Product
1 Find the Dot Product of Two Vectors
-$\mathbf { u } = - 4 \mathbf { i } + 9 \mathbf { j } , \mathbf { v } = - 9 \mathbf { i } + 8 \mathbf { j }$; Find $( 4 \mathbf { u } ) \cdot \mathbf { v }$.
A) 432
B) $- 452$
C) 24
D) 16

Question

Quizplus · Accepted Answer

The dot product of two vectors is found by multiplying the corresponding components and then adding the products. So, for $\mathbf { u } = - 4 \mathbf { i } + 9 \mathbf { j } , \mathbf { v } = - 9 \mathbf { i } + 8 \mathbf { j }$, we have:$$\mathbf { u } \cdot \mathbf { v } = (-4)(-9) + (9)(8) = 36 + 72 = 108$$And for $( 4 \mathbf { u } ) \cdot \mathbf { v }$, we have:$$( 4 \mathbf { u } ) \cdot \mathbf { v } = 4(\mathbf { u } \cdot \mathbf { v } ) = 4(108) = 432$$So, the correct answer is A) 432.

The Dot Product 1 Find the Dot Product of Two u=−4i+9j,v=−9i+8j\mathbf { u } = - 4 \mathbf { i } + 9 \mathbf { j } , \mathbf { v } = - 9 \mathbf { i } + 8 \mathbf { j }u=−4i+9j,v=−9i+8j

The Dot Product
1 Find the Dot Product of Two $\mathbf { u } = - 4 \mathbf { i } + 9 \mathbf { j } , \mathbf { v } = - 9 \mathbf { i } + 8 \mathbf { j }$