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 square,square
angle

Explanation:

Step1: Recall scalar multiplication of vectors

To find \( 5\mathbf{u} \) where \( \mathbf{u} = \langle 2, 7
angle \), we use the rule for scalar multiplication of a vector: if \( \mathbf{u} = \langle a, b
angle \), then \( k\mathbf{u} = \langle ka, kb
angle \) for a scalar \( k \). Here, \( k = 5 \), \( a = 2 \), and \( b = 7 \).

Step2: Apply scalar multiplication

Multiply each component of \( \mathbf{u} \) by 5:
\( 5\mathbf{u} = 5\langle 2, 7
angle = \langle 5 \times 2, 5 \times 7
angle \)
Calculate the components:
\( 5 \times 2 = 10 \) and \( 5 \times 7 = 35 \)
So, \( 5\mathbf{u} = \langle 10, 35
angle \)

Answer:

\( \langle 10, 35
angle \)