Question

For the vectors u= (1, 3, 2) and v=(2, 0, 3)​, evaluate the following expressions.

Answer 1

Answer:

a) 4u + 2v = (8, 12, 14)

b) 2u - v = (0, 6, 1)

c) |u + 4v| = 16.9

Step-by-step explanation:

When we add/subtract vectors, we add/subtract their components. For example

a = (a1,a2,a3)

b = (b1,b2,b3)

a+b = (a1 + b1, a2 + b2, a3 + b3)

|a| is the modulus of vector a, given by

$|a| = \sqrt{a1^{2} + a2^{2} + a3^{3}}$

In this problem, we have that:

u = (1,3,2)

v = (2,0,3)

(a) 4u+2v

4u = 4(1,3,2) = (4,12,8)

2v = 2(2,0,3) = (4,0,6)

4u + 2v = (8, 12, 14)

(b) 2u-v

2u = 2(1,3,2) = (2,6,4)

v = (2,0,3)

2u - v = (0, 6, 1)

(c) |u + 4v|

u = (1,3,2)

4v = 4(2,0,3) = (8,0,12)

u + 4v = (9,3,14)

$|u + 4v| = \sqrt{9^{2} + 3^{2} + 14^{2}} = 16.9$