Let vector b = 5.35 m at 60°. let vector c have the same magnitude as vector a and a direction angle greater than that of vector a by 25°. let vector a · vector b = 30.6 m2 and vector b · vector c = 36.9 m2. find the magnitude and direction of vector a .

The magnitude and direction of vector A are approximately 7.011 meters and 24.670°.

Let be , and , we obtain the magnitude and direction of vector A by definition of dot product:

(1)

(2)

By equalizing (1) and (2), we get the following expression:

If we know that , then we have the following expression:

By (1) we get the magnitude of vector A: (, , )

The magnitude and direction of vector A are approximately 7.011 meters and 24.670°.

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magnitude = 10.8

angle = 118 degree

Explanation:

Magnitude of vector B is 5.35 m and angle is 60 degree

so we have

Now let the magnitude of vector A is "x" and it makes and angle theta

so we have

now for vector C we have

now we know that

also we know that

now we have

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