Q10 of 45 Page 1

Write the vector equation of the line given by

Given,

(say)

⇒ x = 3μ + 5 ; y = 7μ – 4 and z = 2μ + 6

As any random vector is given by –

Putting the values of x, y and z derived from a cartesian form of a line.

⇒

Vector equation of the line given by is given by -

Write the direction-cosines of the line joining the points (1, 0, 0) and (0, 1, 1)

Write the projection of the vector on the vector

Let f : R → R be defined as f(x) = 10x + 7. Find the function g : R → R such that
gof = fog =I_R.

A binary operation * on the set {0, 1, 2, 3, 4, 5} is defined as:

Show that zero is the identity for this operation and each element ‘a’ of the set is invertible with 6–a, being the inverse of ‘a’.

Prove that: