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Find vecA + vecB and vecA - vecB if vec...

Find `vecA + vecB` and `vecA - vecB` if `vecA` make angle `37^@` with positive x-axis and `vecB` make angle `53^@` with negative x-axis as shown and magnitude of `vecA` is 5 and of B is 10.

Text Solution

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So the magnitude of resultant will be = `sqrt(11^2 + (-2)^(2)) = 5sqrt(5)`
and have angle `theta = tan^(-1)(11/2)` from negative x-axis towards up for `vecA - vecB`

So the magnitude of resultant will be
`sqrt(10^2 + (-5)^(2)) = 5sqrt(5)`
and have angle `theta = tan^(-1)(5/10)` from positive x-axis towards down.
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