SOLUTION: The velocity vector v makes an angle of 150 degrees with the positive x-axis and is such that |v| = 5. Find v, giving your answer in the form k√ai + bj, where a and b are real nu

The black vector v is 5 units long.

The right triangle formed is a 30-60-90 right triangle.
Its hypotenuse is 5, the length of the black vector.
The length of the short leg, the red vector, is 1/2 the hypotenuse or 5/2.
It is +5/2 because it goes up.
The length of the long leg, the green vector, is √3 times the short leg,
which is -(5/2)√3.
It is negative because it goes left.

The black vector is the vector sum of the green vector plus the red vector.

The green vector is i.

The red vector is j 

So

v = i + j  <--ANSWER

Edwin