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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​

User Aminhotob
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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.

User Robin Dehu
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