A few days ago
Cantthinkofanickname

What is the magnitude of A – B vector?

Vector A has a magnitude of 12 and points

in the positive x-direction. Vector B has a

magnitude of 15 and makes an angle of 36`

with the positive x-axis.

What is the magnitude of A – B vector?

Top 1 Answers
A few days ago
Anand S

Favorite Answer

Draw a picture to help you. A lies along the x-axis and is 12 units long. B is 36 degrees counter-clockwise from there and is 15 units long.

Since you are adding A and -B (not regular B), you would draw a copy of B starting from the tip of A, but facing in the opposite direction as before (with the arrow pointing towards the third quadrant). Then draw an arrow from the origin to the end of -B to see what your resultant vector, A-B, looks like.

To find the magnitude, you need to split both vectors A and -B into components. Remember that you add the x-components of both vectors together to get the x-component of A-B, and you add the y-components of A and -B together to get the y-component of A-B.

The x-component is magnitude*cos(theta), where theta is the angle with respect to the x-axis. Since A lies along the x-axis, its theta is 0 degrees. B has a theta of 36 degrees, but you want -B. From your picture you can see that you can get -B by rotating B a certain number of degrees. Can you figure out what the theta for -B is?

The y-component is magnitude*sin(theta). Once you have all the components, add the appropriate ones to get the final x-component and final y-component of A-B.

Finally, remember that the magnitude is found by pretending that the components are the sides of a right triangle. So we use the Pythagorean Theorem to get the magnitude of the resultant vector. Magnitude^2 = (x-component)^2 + (y-component)^2

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