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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

The correct Answer is:
(a) 6m and 3m
(b) `sqrt(45)` m
(c) `tan^(-1)((1)/(2))`
`" "because A_x = 4, A_y = 6 ` so ` A_x+ B_x=10` and `A_y+B_y=9`
(a) `B_x= 10 -4 = 6`m and `B_y= 9-6=3`m
(b) length = `sqrt (B_x^(2)+ B_y^(2)) = sqrt (36+9) = sqrt (45)` m
(c) `theta = tan^(-1)((B_y)/(B_x))= tan^(-1) ((3)/(6)) = tan^(-1) ((1)/(2))`
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