Question

Help PLease. A vector is defined as having magnitude of 15 m and a direction of East. Multiply this vector by the scalar value of –6. What is the resultant vector’s magnitude and direction?

What are the components of a vector C→ if its magnitude is 8.9 m/s and it makes an angle of –40° with the +x-axis?

Answer 1

• 90 m West
• (6.82, -5.72) m/s

Explanation:

1. The magnitude of the multiplier is 6, so the magnitude of the new vector is 6×(15 m) = 90 m. The sign on the multiplier is negative, so the new vector will be in the opposite direction of East. It will be 90 m West.

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2. The components can be found from ...

(8.9 m/s)(cos(-40°), sin(-40°)) ≈ (6.82, -5.72) m/s

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One or both of the components will usually be irrational if the angle is a rational number of degrees not a multiple of 90°. Here, we have rounded to 2 decimal places.