Vectors

Question 1

How to find unit vector?

Answer 1

Divide my the mod

Question 2

Vector form of a line?

Answer 2

r = a + ;\AB

Question 3

Parametric form of a line?

Answer 3

x = 5+2;\
y = -2-;\
z = 4+3;\

Question 4

Cartesian form of a line?

Answer 4

x-5 = y+2 = z-4
—- - —- ——
2. 1. 3

Question 5

Scalar product forms of a plane?

Answer 5

r . ñ = d
r . n = D

r . ñ = a . ñ
(a = position vector of a point)

Question 6

Cartesian forms of a plane?

Answer 6

If ñ = Li + Mj + Nk
L^2 + M^2 + N^2 = 1

Lx + My + Nk = d
Ax + By + Ck = D

Question 7

Parametric forms of a plane?

Answer 7

r = a + ;\ d + /u\ e
(Contains point a)
(Plane parallel to vectors d and e)

r = ;\ a + /u\ b + /n\ c
(Contains points A B C)
( ;\ + /u\ + /n\ = 1)

Question 8

What are Skew lines?

Answer 8

Not parallel and don’t intersect

Question 9

Distance of a point from a plane?

Answer 9

a . ñ - d
(a is position vector of point)
( ñ is unit vector of plane)
( d is distance of plane from origin)

Question 10

Angle between 2 planes?

i.e angle between ñ1 and ñ2

Answer 10

Cos@ = ñ1 . ñ2

Question 11

Angle between a line and a plane?

Answer 11

@ = 90 - ¥
(@ is angle between line and plane)

Cos¥ = b . ñ
——-
|b|
(b is the direction of the line)

Question 12

Distance between a line and a plane?

If parallel

Answer 12

1) Find plane in form r.ñ = d
( d = distance of plane from origin)
2) Use a point on the line to find the plane containing L and parallel to Pi
r.ñ = a . ñ
(a = point on the line)
Rearrange to get r.ñ = d
(d= distance of this plane from origin)
3) distance = d1 + d2

Question 13

Angle between two straight lines?

Answer 13

Tan& = M1-M2
—————-
1 + M1M2
(M = gradient)