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?

1 Answer
Jan 15, 2018

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
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