MATH151 Week in Review 1.1-1.2

1. Given the point P(3,-4), find the point Q so that the vector from P to Q is equivalent to the vector a=6i+2j.

2. Given the vectors a=-3i-4j and b=5i-2j, find a unit vector in the

direction of 2a+b.

3. Find scalars m and n such that m< -1,2> + n< -3,-4> = < 5,6>.

4. A man walks due west at 3 mph on a ship which is travelling 20mph northwest (45 degrees west of north). Find the speed and direction (angle due north) of the man relative to the water.

5. Two people pull ropes attached to a 50 kg box (on a frictionless surface). The forces on the box are F1=20N at N60ᵒE and F2=30N at S45ᵒE. Find the magnitude and angle of the acceleration of the box.

6. (1.2)Let u and v be orthogonal unit vectors and w=u+v. Find u·w.

7. (1.2) Find the angle between the vectors 3i-5j and -i-2j.

8. (1.2) Given the points A(4,1), B(-2,-3) and C(5,0), find the cosine of angle BAC.

9. (1.2) Find the scalar and vector projections of -2i+j onto 3i+4j.

10. (1.2) A boy pulls a wagon in a straight line for a distance of 5 miles with a force of 10N. If the wagon arm makes an angle of 30ᵒ, how much work is done?

11. Find the distance from the point (2,5) to the line 2x -y =4.