vectors

Question 1

how to test if two vectors are orthogonal

Answer 1

the dot product will be 0 as the angle is 90 degrees

Question 2

scalar product

Answer 2

a . b = |a||b|cosx

Question 3

unit vector

Answer 3

u/|u|

Question 4

vector product

Answer 4

determinant of a matrix

Question 5

what angle will be between two parallel vectors

Answer 5

0 or pie

Question 6

sinx formula

Answer 6

|a x b|= |a||b|sinx

Question 7

what does doing the vector product find

Answer 7

the area
finds the normal of two vectors

Question 8

triple scalar product

Answer 8

(a x b) . c

Question 9

when are 3 vectors coplanar

Answer 9

(a x b) . c = 1

Question 10

triple vector product

Answer 10

a x (b x c)
Finds volume

Question 11

equation of a line

Answer 11

r = a + tu

Question 12

how do you find u for the equation of a line

Answer 12

b - a

Question 13

distance formula

Answer 13

y = sqrt((x1 - x2) + (y1 - y2))

Question 14

vector equation of a plane

Answer 14

( r - a) . n = 0

Question 15

how to find line POI

Answer 15

• write the 2 line equations in cartesian form
• solve for t
• substitute t into cartesian equation
• this gives the POI

Question 16

how to find plane POI

Answer 16

• find cartesian equation of the line
• sub these values in the equation of the plane
• find the value of t
• if t disappears the line and plane are parallel
• sub t into equation of the line to get POI

Question 17

angle between a line and a plane

Answer 17

use the dot product of direction vector of the line and normal of the plane

Question 18

angle between 2 planes

Answer 18

cos x = n1 . n2 / |n1||n2|

• if n1 . n2 is positive the angle is acute so the angle is pie/2 - angle
• • if n1 . n2 is negative the angle is obtuse so the angle is angle - pie/2

Question 19

how to find the minimum distance with a point and a plane

Answer 19

• write line equation in cartesian form
• sub these into plane equation
• find t and sub into cartesian line equation
• this is the POI
• use the original point and the POI and find the distance between them

Question 20

how to find the minimum distance with 2 planes

Answer 20

• find a point on one P1 by substituting y=z=0
• find the line equation normal to P2 passing through the point we found
• do the same process as line and plane