Question

given vectors u and v, find (a) 5u, (b) 5u + 4v, and (c) v - 4u.
u = \langle 2,7 \
angle
v = \langle 9,0 \
angle
(a) 5u = \langle 10, 35 \
angle
(b) 5u + 4v = \langle 46, 35 \
angle
(c) v - 4u = \langle \square, \square \
angle

Explanation:

Step1: Find 4u

To find \( 4\mathbf{u} \), we multiply each component of \( \mathbf{u} = \langle 2, 7
angle \) by 4.
\( 4\mathbf{u} = \langle 4 \times 2, 4 \times 7
angle = \langle 8, 28
angle \)

Step2: Subtract 4u from v

To find \( \mathbf{v} - 4\mathbf{u} \), we subtract the corresponding components of \( 4\mathbf{u} \) from \( \mathbf{v} = \langle 9, 0
angle \).
For the x - component: \( 9 - 8 = 1 \)
For the y - component: \( 0 - 28 = - 28 \)
So \( \mathbf{v}-4\mathbf{u}=\langle1, - 28
angle \)

Answer:

\( \langle 1, -28
angle \)