Question

If a vector + b vector is equal to c vector and their respective magnitudes are 5 4 and 3. what is the angle between a vector c vector?

​

Answer 1

Explanation:

Given that vector A + vector B = vector C and their respective magnitudes are 5, 4 and 3.

We need to find the angle between vector A and vector C.

vector A + vector B = vector C

vector C - vector A = vector B

Also given that,

• vector A = 5
• vector B = 4
• vector C = 3

So,

vector C - vector A = √[(vector C)² + (vector A)² - 2 × vector C × vector C)]

| vector B |² = | vector C - vector A |²

| vector B |² = | (vector C)² + (vector A)² - 2 × vector C × vector A | cosØ

(4)² = (3)² + (5)² - 2(3)(5) cosØ

16 = 9 + 25 - 30cosØ

16 = 34 - 30 cosØ

30 cosØ = 34 - 16

30 cosØ = 18

cosØ = 18/30

cosØ = 3/5

Ø = cos-¹ (3/5)

Therefore, the angle between the vector A and vector C is cos-¹ (3/5).

Answer 2

Explanation:

Vector C - Vector A = [(Vector C)² + (Vector A)² - 2 x Vector C × Vector C)]

| Vector B 1² = | Vector C - Vector A 1²

| Vector B 1² = | (Vector C)² + (Vector A)² - 2 × Vector C x Vector A l Cos ∅

(4)² = (3)² + (5)² - 2(3)(5)∅

Cos 16 = 9 + 25 - 30cos theta

16 = 34 - 30cos theta

30 cos = 34 - 16

30 cos = 18

cos theta = 18/30

cos theta = 3/5

∅= cos-¹ (3/5).