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

See attached file.

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.

Solution:

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.