Math 22 Exam 1

Front 1

dot product a*b=?

Back 1

x1x2+y1y2+z1z2

Front 2

cross product aXb=?

Back 2

a2b3-a3b2, a3b1-a1b3, a1b2-a2b1

Front 3

angle between two vectors =?

Back 3

|a X b| =|a|*|b|*sin(theta) or a*b=|a|*|b|cos(theta)

Front 4

angle between two intersecting lines =?

Back 4

Break down to parametric equations, then use |a X b| =|a|*|b|*sin(theta) or a*b=|a|*|b|cos(theta)

Front 5

when cross product = 0...

Back 5

vectors are parallel

Front 6

Angle between two intersecting planes?

Back 6

Find normal vectors, then use |a X b| =|a|*|b|*sin(theta) or a*b=|a|*|b|cos(theta)

Front 7

equation of line of two intersecting planes?

Back 7

set one variable equal to 0, then solve for the other 2 variables. solve for the cross product of the normal vectors, which yields the directional vector.

Front 8

equation of a line containing two points a and b?

Back 8

take a-b to get direction vector. then choose either point to make parametric equations

Front 9

equation of a line that's perpendicular to a plane and containing a certain point?

Back 9

take normal vector of the plane, then make parametric equation using the given point.

Front 10

equation of a line parallel to a given line and intersecting a certain point?

Back 10

Find the direction vector of the line, then write vector equations.

Front 11

equation of a line tangent to a curve at a given point?

Back 11

g

Front 12

equation of a plane containing points abc?

Back 12

take vector ab and ac and cross them to get DEF. then use D(x-a1)+E(y-a2)+F(z-a3)=0

Front 13

equation of a plane using two non skew lines?

Back 13

find a point P on one line, then find two points Q and R on the other line. cross PQ and PR then use plane equation.

Front 14

equation of a plane containing a point and a line?

Back 14

Find two points on the line and make vectors to the point. cross these vectors and use the plane equation.

Front 15

equation of a plane parallel to another plane and containing point P?

Back 15

Find the direction vector of the plane, then use D(x-P1)+E(y-P2)+F(z-P3)=0.

Front 16

Area of a triangle =?

Back 16

1/2 times the magnitude of the cross product.

Front 17

distance from point x,y,z to plane?

Back 17

use D=(ax+by+cz+d)/(sqrroot(a^2+b^2+c^2)

Front 18

|a|*|b|cos(theta) =?

Back 18

a*b

Front 19

|a|*|b|sin(theta) =?

Back 19

|aXb|