Answered

Select the correct answer.

If [tex]\( \mathbf{w} = \langle 3.5, -6 \rangle \)[/tex] and [tex]\( \mathbf{z} = \langle -1.5, -4 \rangle \)[/tex], what is the resulting vector for [tex]\( 2\mathbf{w} - \mathbf{z} \)[/tex]?

A. [tex]\( \langle 5, -2 \rangle \)[/tex]

B. [tex]\( \langle 10, -4 \rangle \)[/tex]

C. [tex]\( \langle 8.5, -8 \rangle \)[/tex]

D. [tex]\( \langle 5.5, 12 \rangle \)[/tex]



Answer :

GinnyAnswer
Sure, let's work through the problem step-by-step.

We are given the vectors [tex]\( w = \langle 3.5, -6 \rangle \)[/tex] and [tex]\( z = \langle -1.5, -4 \rangle \)[/tex]. We need to find the resulting vector for [tex]\( 2w - z \)[/tex].

1. Calculate [tex]\( 2w \)[/tex]:

Let's start by multiplying vector [tex]\( w \)[/tex] by 2:
[tex]\[ 2w = 2 \times \langle 3.5, -6 \rangle = \langle 2 \times 3.5, 2 \times (-6) \rangle \][/tex]
Calculate each component:
[tex]\[ 2 \times 3.5 = 7, \quad 2 \times (-6) = -12 \][/tex]
So,
[tex]\[ 2w = \langle 7, -12 \rangle \][/tex]

2. Calculate [tex]\( 2w - z \)[/tex]:

We need to subtract vector [tex]\( z \)[/tex] from [tex]\( 2w \)[/tex]:
[tex]\[ 2w - z = \langle 7, -12 \rangle - \langle -1.5, -4 \rangle \][/tex]
To subtract [tex]\( z \)[/tex], subtract each corresponding component:
[tex]\[ 2w - z = \langle 7 - (-1.5), -12 - (-4) \rangle \][/tex]
Simplify the components:
[tex]\[ 7 - (-1.5) = 7 + 1.5 = 8.5 \][/tex]
[tex]\[ -12 - (-4) = -12 + 4 = -8 \][/tex]

3. Resulting vector:

The resulting vector is:
[tex]\[ 2w - z = \langle 8.5, -8 \rangle \][/tex]

So, the correct answer is:
C. [tex]\(\langle 8.5, -8 \rangle\)[/tex]

Other Questions