Find a vector v whose magnitude is 20 and whose component in

Find a vector v whose magnitude is 20 and whose component in the i direction is five times the component in the j direction.

Solution

|v| = 20

v = xi + yj . Now x = 5y

So, angle = tan^-1(y/x) = tan^-1(1/5)

tan(theta) = 1/5 ; So, cos(theta) = 5/sqrt26 ; sin(theta) = 1/sqrt26

Now x = 20cos(theta) = 100/sqrt26 ; y = 20sin(theta) = 20/sqrt26

v = xi + yj = i100/sqrt26 + j20/sqrt26