A) Vector A = 3i – 4j. What is vector –A? If vector B = -2i +3j, find vector A+B

Question

A) Vector A = 3i – 4j. What is vector –A? If vector B = -2i +3j, find vector A+B and vector A-B. Draw these vectors. What are |A+B| and |A-B|?

B)I start from town A and walk 30 degrees with respect to due east for 20 km and arrive at town B. Then I walk another 10 km at an angle of 30 degrees with respect to AB vector, and I arrive at town C. From town C, I proceed 20 km due west and arrive at town D. (a) Find the distance of town D from town A (the magnitude of AD vector) and (b) the angle ADC using the scalar product. (c) Find the angle using the vector product.

Explanation / Answer

A)

A = 3i – 4j, B = -2i +3j

Now -A = -3i + 4j

A + B = i - j

A - B = 5i - 7j

|A+B| = sqrt(1 + 1) = sqrt(2)

|A-B| = sqrt(25 + 49) = sqrt(74)

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