Question

find u + v - 5u.
u = \langle 7, - 3 \
angle and v = \langle - 4,8 \
angle
u + v - 5u = \langle \square,\square \
angle

Explanation:

Step1: Simplify the vector expression

First, simplify \( \mathbf{u} + \mathbf{v} - 5\mathbf{u} \) by combining like terms. We know that \( \mathbf{u} - 5\mathbf{u}=- 4\mathbf{u} \), so the expression becomes \( \mathbf{v}-4\mathbf{u} \).

Step2: Substitute the given vectors

Given \( \mathbf{u}=\langle7, - 3
angle \) and \( \mathbf{v}=\langle-4,8
angle \), we need to find \( - 4\mathbf{u} \) first. To find \( - 4\mathbf{u} \), we multiply each component of \( \mathbf{u} \) by - 4.
For the x - component: \( - 4\times7=-28 \)
For the y - component: \( - 4\times(-3) = 12 \)
So, \( - 4\mathbf{u}=\langle-28,12
angle \)

Step3: Add \( \mathbf{v} \) and \( - 4\mathbf{u} \)

Now, add \( \mathbf{v}=\langle-4,8
angle \) and \( - 4\mathbf{u}=\langle-28,12
angle \). To add two vectors \( \langle a,b
angle \) and \( \langle c,d
angle \), we add their corresponding components, i.e., \( \langle a + c,b + d
angle \).
For the x - component: \( - 4+( - 28)=-32 \)
For the y - component: \( 8 + 12=20 \)

Answer:

\(\langle - 32,20
angle\)