Review for Test 1 

Sections 10.1-10.6 (Old Book 12.1-12.6)

To Study for Test 1:
1) Try the Old Test 1 Problems
2) Know everything on this test review.
3) Study your homework problems and class notes from these sections.

Formulas given on Test 1: 

projab = a^2*b/abs(a)^2 




For Section 10.1 (Old Book 12.1) you need to: 

1) Memorize the distance formula in 3-D.

2) Memorize the equation of a sphere.

3) Know how to plot points in 3-D. 

4) Know x = c, y = c, z = c are equations of planes and how to graph those planes. 

6) Know x^2+y^2 = c is an equation of a circular cylinder and how to graph a circular cylinder.

 7) Know that (x - h)2 + (y - k)2 + (z - l)2 = r2 is a sphere with center (h, k, l) and radius r, and know how to graph a sphere.

 

For Section 10.2 (Old Book 12.2) you need to know:

1) How to add/subtract vectors graphically using "head-to-tail" line-up. 

2) What cv means for c > 0 and c < 0. 

3) How to find the magnitude of a,  | a |. 

4) How to add/subtract vectors and scalar multiples of vectors numerically. 

5) How to find vector PQ, given P = (x1, y1, z1) and Q = (x2, y2, z2). 

6) How to find a unit vector in the direction of a, u = a / | a | 

7) What i, j, k vectors are. 

 

For Section 10.3 (Old Book 12.3) you need to know: 

1) The Dot Product of vectors a and b. 

2) a*b = abs(a)*abs(b)*cos*theta 

3) a and b are orthogonal if a*b = 0. 

4) a is parallel to b if a = cb. 

5) How to find the projab given the formula, projab =  

7) The scalar projection of b onto a is  

compab = a*b/abs(a) 

 

For Section 10.4 (Old Book 12.4) you need to know: 

1) How to find the cross product, a x b. 

2) That c = a x b is perpendicular to both a and b, with the direction determined from the right-hand rule. 

3) Area of the parallelogram formed by a and b, is A =  

4) How to use the volume formula for the volume of a parallelopiped formed by a, b, and c is V =  

 

For Section 10.5 (Old Book 12.5) you need to know: 

1) The vector equation of a line passing through P0(x0, y0, z0) parallel to vector v = < a, b, c > is  

           r(t) = r0 + tv, where r(t) = < x, y, z > and r0 = < x0, y0, z0 > 

2) That parametric equations are of the form x = x0+ ta, y =  y0+ tb, z =  z0+ tc. 

3) That symmetric equations are of the form (x - x0)/a = (y - y0)/b = (z - z0)/c,   

4) That a line segment from P0(x0, y0, z0) to  P1(x1, y1, z1) is given by 

            r(t) = (1 - t)r0 + tr1, where r0 = < x0, y0, z0 >,  r1 = < x1, y1, z1 > and 0 < t < 1 

5) Equation of a plane through P0(x0, y0, z0) with normal vector n = < a, b, c > is given by 

            n*(r-r[0]) = 0 , where r = < x, y, z > and r0 = < x0, y0, z0 > 

or equivalently, 

            a(x - x0) + b(y - y0) + c(z - z0) = 0 

or equivalently, 

            ax + by + cz  + d = 0, where d = -(ax0 + by0 + cz0) 

6) Two planes are perpendicular if their normal vectors are perpendiculars and two planes are parallel if their normal vectors are parallel. 

7) To find the angle between 2 planes, find the angle between their normal vectors. 

8) How to use the distance formula between a point P1(x1, y1, z1) and a plane ax + by + cz + d = 0 

              


For Section 10.6 (Old Book 12.6) you need to know: 

1) Memorize the 3D Surfaces to be able to state the following given an equation:
          a) the name of the surface
          b) the major axis
          c) the center point

2) How to graph planes of the form Ax + By + Cz + D = 0 where either 1 variable is present (e.g. x = 4), or 2 variables are present (e.g. x + y = 4), or all 3 variables are present (e.g. x + y + z + 4).