A vector that is 6.3 units long and a vector that is 5.3 units long are added. T

Question

A vector that is 6.3 units long and a vector that is 5.3 units long are added. Their sum is a vector 11.1 units long. Show graphically at least one way that the vectors can be added. (Do this on paper. Your instructor may ask you to turn in this work.) Using your sketch in Part(a), determine the angle between the original two vectors. degree Calculate the unit vector (in terms of cap i and cap j) in the direction opposite to the direction of each of the following vectors. Vector A = 3.6 cap i + 4.5 cap j, vector B = (-8.5) cap i + 3.5 cap j, and vector C = 5.1 cap i + (-8.9)cap j. - cap A = -cap B = -cap C = The unit vector in the direction opposite to the direction of a vector is found by taking the negative of the unit vector in the direction of the vector. The unit vector in the direction given vector is found by dividing the given vector by its magnitude.

Explanation / Answer

the unit vector in the direction opposite to the direction of each of the vectors are

-A = -(3.6i + 4.5 j) / sqrt(3.6^2 + 4.5^2) = - (0.62i + 0.78j)

-B = -(-8.5i +3.5j) / sqrt(8.5^2 + 3.5^2) = (0.92i -0.38j)

-C = -(5.1i -8.9j) / sqrt(5.1^2 + 8.9^2) = (-0.47i + 0.87j)

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