Vector A has a magnitude of 27 m and points in a direction 32° above the positive x axis. Vec-
tor B has a magnitude of 35 m and points in a direction
55° below the positive x axis. Sketch the vectors A, B,
and C = A + B. Estimate the magnitude and the
direction angle of from
your
sketch.

The magnitude of the resultant is 55.0 m

The angle of resultant is 18.4°  below the x axis

Explanation:

Given that,

Magnitude of vector A = 27 m

Angle = 32° above the x axis

Magnitude of vector B = 35 m

Angle = 35° blow the x axis

We need to calculate the angle between the vectors

Using given angle

ptex]\theta=87^{\circ}[/tex]

We need to calculate the sum of vector A and B

Using formula of sum of vector

Put the value into the formula

We need to calculate the direction angle

Using formula of angle

Put the value into the formula

We need to calculate the angle of the resultant vector makes with vector A

Using formula of angle

Negative sign shows that the direction of resultant is below the x axis

Hence, The magnitude of the resultant is 55.0 m

The angle of resultant is 18.4°  below the x axis

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