Vectors

Question 1

Equation of line passing through (a1,a2,a3) in direction (u1,u2,u2) in vector form

Answer 1

r = (a1)………..(u1)
……(a2)+…..λ(u2)
……(a3)……….(u3)

Question 2

Equation of line passing through (a1,a2,a3) in direction (u1,u2,u2) Cartesian form

Answer 2

(x-a1)/u1 = (x-a2)/u2 = (x-a3)/u3

Question 3

angle between to vectors is given by

Answer 3

Cosθ = a.b / |a|.|b| 
|a| = sum of the xyz components squared and square rooted

Question 4

the Cartesian equation for a plane perpendicular to (n1) ……………………………………………………………………………………..(n2)
……………………………………………………………………………………..(n3)

Answer 4

(n1)X + (n2)Y + (n3)Z + d = 0

Question 5

the vector perpendicular to the plane (n1)X + (n2)Y + (n3)Z + d = 0

Answer 5

(n1)
(n2)
(n3)

Question 6

Distance of a point from a plane is found by

Answer 6

construct a line perpendicular to the plane and through the given point , find where the line intersects the plane, find the distance between the two points