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    Vector A in polar coordinates, vector B in unit vectors: Find vector sum difference.

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    Vectors A in polar coordinates and vector B with unit vectors are given. Find a vector sum and a vector difference. Ignore units.

    Vector A= 5 units at 53 degrees, and B= 5 i - 2 j in which i and j are unit vectors in x and y directions respectively.

    PART a. Show A and B and vector sum C in a polygon (Not to scale) showing A + B = C.
    SEE ATTACHMENT #1 for a diagram showing known data for A and B, and also a general triangle for showing law of cosines and law of sines.

    PART b. Use the law of cosines to calculate the magnitude of C.

    PART c. Express A with unit vectors, then find D with unit vectors, if D= B - A.

    PART d. Using the answer to part c, construct a vector polygon (Not to scale) having D, B and A connected to show D= B - A.

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    Solution Preview

    See attached file.


    PART a. Step 1.
    Recall that vectors connected head-to-tail are added vectors, and their vector sum is the vector from the tail of the first to the head of the last vector. This arrangement is shown in ATTACHMENT #2. Notice that A and B are head to tail and C is from the tail of A to the head of ...

    Solution Summary

    The vector A in polar coordinates and vector B in unit vectors are determined. With a graph and good explanations, the problems are solved.