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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

`because A_(x)=4, A_(y)=6` so `A_(x)+B_(x)=10` amd `A_(y)+B_(y)=9`
(a) `B_(x)=10-4=6m` and `B_(y)=9-6=3m`
(b) length `=sqrt(B_(x)^(2)+B_(y)^(2))=sqrt(36+9)=sqrt(45m)`
(c) `theta=tan^(-1)((B_(y))/(B_(x)))=tan^(-1)((3)/(6))=tan^(-1)((1)/(2))`
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