A vector A has a magnitude of 14 (in some unspecified units) and makes an angle

Question

A vector A has a magnitude of 14 (in some unspecified units) and makes an angle of 24° with the x-axis, and a vector B has a magnitude of 26 and makes an angle of 70° with the x-axis. Compute the magnitudes and directions of the vectors (a) C=A+B magnitude direction 37.1 2 67 X(counterclockwise from the +x-axis) (b) C-A- B magnitude direction 3 19.1 281.75 (counterclockwise from the +x-axis) (c) C=A+ 4B magnitude direction 114.17 64.94 (counterclockwise from the +x-axis) (d) C=-A-7B magnitude direction 191.99 8 -67 X(counterclockwise from the +x-axis)

Explanation / Answer

For example, if you have two vectors P and Q, its resultant magnitude is given by

R 2 = P 2 + Q 2 + 2PQ cos (?)

R = root of [ P2 + Q2 + 2PQ cos ? ]

The direction of R can be obtained by

Q / sin ? = P / sin ? = R / sin ?

? - angle between A and B vectors

[This is Triangular law of vectors]

Another example:

R2 = P2 + Q2 + 2PQ cos ?

R = Root of [ P2 + Q2 + 2PQ cos ?]

? = tan-1 [ Q sin ? / (P+Qcos ?) ]

[ This is Parallelogram law of vectors]

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