# Standard Position

Answer the following given the two vectors written in standard position.

A⃗ = 4m/s@220o B⃗ = 7m/s@300o

a) Draw a diagram for A⃗ and write A⃗ in terms of î and ĵ (answer to 2 decimal places). (2 marks)

b) Draw a diagram for B⃗ and write B⃗ in terms of î and ĵ (answer to 2 decimal places). (2 marks)

c) Determine the angle θ between A⃗ and B⃗ using the dot product. Then draw a diagram and use geometry to verify your answer. (3 marks)

nswer the following given the two vectors (measured in meters).

A⃗ = −4̂i+ 10ĵ + k̂ B⃗ = 5̂i+ 5k̂

a) Using only the dot product (no cross products) determine a unit vector Ĉ that is perpendicular

to both A⃗ and B⃗. I recommend checking that your answer is indeed perpendicular to both A⃗ and B⃗ by taking a dot product with each. (6 marks)

b) Determine the angle ϕ (Greek letter for F, pronounced ’f-eye’) between Ĉ and the z-axis (answer to 2 decimal places). (2 marks)

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