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The x and y-components of vector A are 4...

The x and y-components of vector A are 4 m and 6 m respectively. The x and y-components of vector A + B are 10 m and 9 m respectively. Calculate for the vector B the following:
(a) its x and y-components
(b) its length
(c ) the angle it makes with x-axis.

Text Solution

Verified by Experts

In terms of components
`vecA + vecB =(hati A_(x) + hatj A_(y)) + (hati B_(x) + hatj B_(y))`
i.e., `vecA + vecB =hati (A_(x) + B_(x)) + hatj (A_(y) + B_(y))`
According to given problem ,
`A_(x) + B_(x) = 10 and A_(y) + B_(y) = 9`
and `" "A_(x)= 4 and A_(y)= 6`
So, (a) `B_(x) = 10- 4 = 6m and B_(y) = 9- 6=3m`
(b) `b=sqrt(B_(x)^(2)+ B_(y)^(2))= sqrt(6^(3) + 3^(2))= sqrt(45)= 3sqrt(5)m`
(c) `theta = tan^(-1)[(B_(y))/(B_(x))] = tan^(-1)[(3)/(6)]= tan^(-1)[(1)/(2)]`
`= 26.60^(@)`
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