Precalculus
Name
Period
Date
Chapter 10
Review Test
The following formulas may be needed for this test:
cos  
uv
 u  v 
For Questions involving P and Q as points, always use: P (3, 5, 6) and Q (-8, 5, -7)
For Questions involving the A Vector, use: A <3, 5, 6>, and the B Vector, use: <-8, 5, -7>
1. Determine the distance between P and Q. Round to 2 decimal places.
1.
____________
2.
____________
2. Determine the midpoint between P and Q and state your answer as a point.
3. Write the general equation for a sphere using X, Y, and Z as variables and A through G
as constants.
3. ___________________________________________
4. Write the standard equation for a sphere using X, Y, and Z as variables and H, K, J, and R
as constants.
4. ______________________________
5. Write the following general equation in the standard form for a sphere, and then give
the sphere’s center point and magnitude of the sphere’s radius:
X2 + Y2 + Z2 – 2X – 2Y – 4Z +2 = 0
5. Equation____________________________________
Center Point ___________________________________
Magnitude of Radius ____________________________
Write the following standard equation in the general form for a sphere
(X – 2)2 + (Y – 4)2+ (Z + 3)2 = 16
_____________________________________________
6. Write the vector PQ using i, j, and k as vector components
6. _________________
7. Determine the magnitude of the PQ vector. Round to two decimals.
7. _________________
8. A vector’s magnitude is 20 units, the angle it makes with the Y axis is 60 degrees and
with the X axis is 30 degrees, state the vector in i, j, and k components. Round to 2 decimals.
8. _________________
9. Determine the sum of the A and B vectors and state the answer as a vector
using i, j, and k components
9. _________________
10. An velocity vector can be determined by multiplying time (a scalar) by an acceleration vector.
State (with units) the velocity vector (using I, j, and k components) of an object subjected to an
acceleration vector of <1, -1, 2> m/s2 for .05 hours
10. _______________________________
11. State the final speed of the above object assuming its initial speed was zero (round to 2 decimals
and include the units)
11. ________________
12. Work is defined as the dot product of a force applied to an object as the force is displaced.
Determine the work done by the force F <5, 5, 10> in Newtons on the object as the force is
displaced <5, 10, 0> Meters. (disregard units in your answer)
12. ________________
13. Determine the angle in degrees (round to 2 decimals) between the A and B vectors
13. ________________
14. Given two vectors <6, -8, 2> and <-2, -1, 2> state if the vectors are parallel, orthogonal, or neither (circle one).
Show work for full credit
Given two vectors <6, -8, 2> and <-3, 4, -1> state if the vectors are parallel, orthogonal, or neither (circle one).
Given two vectors <6, -8, 2> and <8, -10, 4> state if the vectors are parallel, orthogonal, or neither (circle one).
15. You wish to bring an object into equilibrium, but it has two force vectors acting on the
object F1 <5, 10, 7> and F2 <-10, 4, 0>. Determine the equilibrant needed to bring the object
into equilibrium. State the Force vector in component form, then give its magnitude, and angle
(in degrees) with respect to the +X axis in the XY plane.
15. Vector ______________________
Magnitude ______________________
Angle __________________________
16. Determine A X B use i, j, and k components
16. ______________________
17. True or False (circle one), a parallelogram’s area has a direction
18. True or False (circle one), the volume of an object has a direction
19. Two vectors R and S whose magnitude is 10 and 5 respectively are at an angle
of 60 degrees to each other, determine the magnitude of R X S (no units)
19. _______________
20. If the vector R is 10j and the vector S is -20k, state the direction
(give the component(s) with + or -) of S X R
20. _________
21. True or False (circle one) c(A X B) = c(B X A) (c is a scalar quantity and A and B are vectors)
22. Determine the volume (no units) of the parallelepiped described by the three vectors:
H <2i, -10j, 1k>, L <2i, 2j, -2k> and M <5i, 2j, -2k>
22. _____________