Question

3 Consider two vectors Az 31 - 2; and Bz-i-4;. alculated B C) A+B and A-B B G) / Atb 1 and (A-Blu | - B (i fra) Direction of (A+B) and|A-b] B) B + ดู B BJ​

Answer 1

Explanation:

1. A+B=Just add the J hat with J hat and add the I hat with the I hat.

`(3i + ( - 1)i + ( - 2) + ( - 4)j = 2i - 6j`

A-B=

`3 - ( - 1)i + ( - 2) - ( - 4)j = 4i + 4j`

2. Take the magnitude of A+B

`2 {}^(2) + ( - 6) {}^(2) = {r}^(2)`

`40 = {r}^(2)`

`r = √(40)`

So the magnitude is root of 40.

So the magnitude of A+B is

The magnitude of A-B

`{4}^(2) + {4}^(2) = 4 √(2)`

So the magnitude is

`4 √(2)`

c. To find direction, we need to find the angle.

Use this rule,

`\tan(x) = (bj)/(bi)`

For A+B, we get

`\tan(x )= ( - 6)/(2)`

`\tan(x) = - 3`

Since this is a southeast, the degree is 288.43.

The direction is southeast, 288.43 degrees

For A-B, we get

`\tan(x) = (4)/(4)`

`\tan(x) = 1`

Since this is northeast, the degree is 45 degrees.

The direction is northeast, 45 degrees.