Find the direction and magnitude of the vectors Part A Find the magnitude of the

Question

Find the direction and magnitude of the vectors

Part A

Find the magnitude of the vector A?  = (5.2m )x^ + (-0.90m )y^.

Express your answer using two significant figures.

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Part B

Find the direction of the vector A?  = (5.2m )x^ + (-0.90m )y^.

Express your answer using two significant figures.

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Part C

Find the magnitude of the vector B?  = (-0.70m )x^ + (5.4m )y^.

Express your answer using two significant figures.

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Part D

Find the direction of the vector B?  = (-0.70m )x^ + (5.4m )y^

Express your answer using two significant figures.

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Part E

Find the magnitude of the vector A? +B? .

Express your answer using two significant figures.

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Part F

Find the direction of the vector A? +B? .

Express your answer using two significant figures.

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Explanation / Answer

Part A)

Magnitude, from the Pythagorean Theorem...

Magnitude2 = (5.2)2 + (.9)2

Magnitude = 5.3 m

Part B)

For the direction...

tan(angle) = .9/5.2 =

Angle = 9.8o Counter clockwise from the x axis

To find the clockwise direction, subtract from 360

360 - 9.8 = 350o

Part C)

Magnitude2 = (.7)2 + (5.4)2

Magnitude = 5.4 m

Part D)

tan(angle) = 5.4/.7

Angle = 82.6o Above the negative x axis

To get clockwise from the positive x axis, subtract from 180

180 - 82.6 = 97o

Part E)

A + B...

The x components are 5.2 - .7 = 4.5 m

The y components are 5.4 - .9 = 4.5 m

The net = sqrt[(4.5)2 + (4.5)2]

Net Magnitude = 6.4 m

Part F)

Since each compomnent is the same length, the net angle is 45o

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