More practice questions

4. Q4. A force of 50 N acts at 150° to the +x-axis. Find its components.

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   F_x = 50 cos 150° ≈ −43.3 N; F_y = 50 sin 150° = 25 N. The negative x-component shows the force points partly in the −x direction.

5. Q5. Find a vector of magnitude 10 units in the direction of 3î − 4ĵ.

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   The unit vector is (3î − 4ĵ)/5 = 0.6î − 0.8ĵ, so the vector is 6î − 8ĵ.

6. Q6. What angle does A = î + ĵ + k̂ make with each axis?

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   A = √3, so cos α = cos β = cos γ = 1/√3 ≈ 0.577, and each angle is about 54.7°.