Question

The question number 3 please.

Answer 1

Explanation:

X-component: 8

Y-component: 12

Z-component: -4

a)

vector A can be written as Ā.

So, Ā = 8 î + 12 j - 4 k

in terms of base Unit vector (Â) = Ā/|Ā|

|Ā| = √[(8² + 12² + (-4)²]

= √(224) = 4√14

 = (8 î + 12 j - 4 k)/(4√14)

 = 2/√14 î + 3/√14 j - 1/√14 k

b) 4 |B| = |Ā|

So, |B| = |Ā|/4

unit vector along B = unit vector along A

(vector B) / |B| = (vector A) / |Ā|

So Vector B = |B| ( Ā / |A| )

vector B = 4( 8 î + 12 j - 4 k)

vector B = 32 î + 48 j - 16 k

c) For two vectors in opposite direction:

unit vector along C = - unit vector along A

[Solve on your own]

Thanks!