Question

given vectors u and v, find (a) 4u (b) 4u + 8v (c) v - 8u.
u=langle 2,5
angle, v=langle 3,0
angle
(a) 4u=langlesquare,square
angle

Explanation:

Step1: Calculate 4u

Multiply each component of u by 4: $4\mathbf{u} = 4\langle 2,5
angle = \langle 4\times2, 4\times5
angle = \langle 8,20
angle$

Step2: Calculate 8v

Multiply each component of v by 8: $8\mathbf{v} = 8\langle 3,0
angle = \langle 8\times3, 8\times0
angle = \langle 24,0
angle$

Step3: Compute 4u + 8v

Add corresponding components: $4\mathbf{u} + 8\mathbf{v} = \langle 8+24, 20+0
angle = \langle 32,20
angle$

Step4: Calculate -8u

Multiply each component of u by -8: $-8\mathbf{u} = -8\langle 2,5
angle = \langle -16,-40
angle$

Step5: Compute v - 8u

Add corresponding components of v and -8u: $\mathbf{v} - 8\mathbf{u} = \langle 3+(-16), 0+(-40)
angle = \langle -13,-40
angle$

Answer:

(a) $\langle 8,20
angle$
(b) $\langle 32,20
angle$
(c) $\langle -13,-40
angle$