Vector Geometry

Question 1

Unit vector

Answer 1

a / |a|

Question 2

Scalar/Dot Product

Answer 2

a.b = |a||b|cosθ

Question 3

Vector equation of a plane

Answer 3

r.n=d

Question 4

Parametric vector equation of a plane

Answer 4

r = a + sb + tc

Question 5

vector product

Answer 5

a x b = |a||b|sinθ

Question 6

scalar triple product and what it represents

Answer 6

a.(bxc) volume of parallelopiped

Question 7

Vector triple product

Answer 7

ax(bxc) = (a.c)b - (a.b)c
(axb)xc = (a.c)b - (b.c)a

Question 8

Shortest distance from point S to line r=a + λc

Answer 8

|SA x c| / |c|

Question 9

Alternative vector equation of line

Answer 9

rxc=d where c is a direction vector

Question 10

Shortest distance between two lines, r1=a + λc, r2=b + μd

Answer 10

(a-b).(cxd) / |cxd| |