Question

Two vectors from an angle of 110°. One of the vectors is 20 units long and makes an angle of 40° with the vector sum of the two. Find the magnitude of the second vector and of the vector sum?

Answer 1

13.71 units

Explanation:

If the sum of two vector `a` and `b` is `C` and that angle between `a` and `b` is `theta` and that of `a` and `C` is `alpha` then the relation is given as,

`tan alpha` = `(b sin theta)/(a + b cos theta)`

Here, `alpha` = 40 degrees
`b` is unknown,`theta` = 110 degrees and `a` is 20 units

Putting all the values we get, `b` is 13.71 units

derivation of the formula is given below