Q19 of 45 Page 1

Evaluate :

Let, I = …(1)

Using the property of definite integral:

∴ I =

⇒ I = {∵ sin (2π – x) = -sin x}

⇒ I =

⇒ I = …(2)

Adding equation 1 and 2, we get –

2I =

Using algebra of integrals we have –

2I =

⇒ 2I = = 2π – 0

∴ I = π

Evaluate:

Evaluate :

If and then find the value of λ, so that and are perpendicular vectors.

Show that the lines

are intersecting. Hence find their point of intersection.

Find the vector equation of the plane through the points (2, 1, – 1) and (– 1, 3, 4) and perpendicular to the plane x – 2y + 4z =10.