Question

given vector \\(\mathbf{u} = \langle -1, -4 \
angle\\) and \\(\mathbf{v} = \langle -4, -5 \
angle\\), determine the value of \\(\mathbf{v} - 3\mathbf{u}\\) in component form.

Explanation:

Step1: Calculate 3u

To find \( 3\mathbf{u} \), we multiply each component of \( \mathbf{u} = \langle -1, -4
angle \) by 3.
\( 3\mathbf{u} = \langle 3 \times (-1), 3 \times (-4)
angle = \langle -3, -12
angle \)

Step2: Calculate v - 3u

To find \( \mathbf{v} - 3\mathbf{u} \), we subtract the corresponding components of \( 3\mathbf{u} \) from \( \mathbf{v} = \langle -4, -5
angle \).
For the x - component: \( -4 - (-3)=-4 + 3=-1 \)
For the y - component: \( -5-(-12)=-5 + 12 = 7 \)
So \( \mathbf{v}-3\mathbf{u}=\langle -1,7
angle \)

Answer:

\(\langle -1, 7
angle\)