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 \square, \square \
angle

Explanation:

Step1: Find 4v

To find \( 4\mathbf{v} \), we multiply each component of \( \mathbf{v} = \langle 9, 0
angle \) by 4. So, \( 4\mathbf{v} = \langle 4\times9, 4\times0
angle = \langle 36, 0
angle \).

Step2: Add 5u and 4v

We already know from part (a) that \( 5\mathbf{u} = \langle 10, 35
angle \). Now, to find \( 5\mathbf{u} + 4\mathbf{v} \), we add the corresponding components of \( 5\mathbf{u} \) and \( 4\mathbf{v} \). That is, for the first component: \( 10 + 36 = 46 \), and for the second component: \( 35 + 0 = 35 \). So, \( 5\mathbf{u} + 4\mathbf{v} = \langle 46, 35
angle \).

Answer:

\( \langle 46, 35
angle \)