Question

Find the angle between V and W, Round your answer to one decimal place, if necessary V=-5i+2j W=-8i+2j A 17.8° B 353.9° C 3.9° D 7.8°

Answer 1

Answer:

D. 7.8°

Step-by-step explanation:

There are many ways to work this problem. One is to subtract the angle of V from that of W:

∠V = arctan(2/-5) ≈ 158.20°

∠W = arctan(2/-8) ≈ 165.96°

Then ∠W -∠V = 165.96° -158.20° = 7.76° ≈ 7.8°

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Another is to divide W by V, since the quotient will have an angle that is the difference of their two angles.

(-8i +2j)/(-5i +2j) = (1/29)(44i +6j)

Then the angle of that is ...

arctan(6/44) ≈ 7.8°

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You can also divide the dot product by the product of the two magnitudes to find the cosine of the angle between the vectors.

(V•W)/(|V|·|W|) = 44/√(68·29) = cos(x)

x = arccos(0.990830168...) ≈ 7.8°

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A plot on graph paper will let you measure the angle with a protractor. You can obtain sufficient accuracy to choose between the offered answers.

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Your graphing calculator may have complex number functions that let you work directly with the angles of the vectors. (See second attachment. The calculator is in degrees mode.) Doing 2-dimensional vector calculations on a calculator may best be accomplished by treating them as complex numbers.