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.

Explanation

(a) Let `vec A = A_x hat i+ A)y hat j= 4 hat i+ 6 hat j`
and `vec B = brv B_x hat i+ B_y hat j`
:. ` vec A+ vec B = ( 4 aht i+ 6 hat j) + (B_x hat i+ B_y hat j)`
` = ( 4 + B_x ) hat I + ( 6 +B_y ) hat j`
According to given problem
` 4+ B_x =10` or ` B_x =10 -4 m`
` 6 + B_y =9 ` or ` B_y =9 - 6 =3 m`
(b) ` B= sqrt (B_x^2+B_y^2) = sqrt 6^2+3^2) = 3 sqrt 5 m`
` (c ) tan theta B_y/B_x = 3/6 = 1/2 = 0.5 = tan 26.6^2` ltbRgt or ` theta = 26.6^2`.