Q16 of 45 Page 1

Using properties of determinants, prove the following:

Given;

Taking x from C₁, y from C₂ and z from C₃

C₁→ C₁ +C₂ + C₃

Taking from C₁

R₂→ R₂ – R₁ and R₃→ R₃ – R₁

Evaluating along C₁

= xyz + xy + yz +zx.

Hence Proved

Find the shortest distance between the following two lines:

vector r = ( i+2 j+3 k ) + lambda ( i-3 j+2 k ) vector r = ( 4+2 μ ) i + ( 5+3 μ ) j + ( 6 + μ ) k

Form the differential equation representing the family of curves given by (x - a)² + 2y² = a², where a is an arbitrary constant.

If y = e^x(sin x + cos x), then show that

Find the area of the region bounded by the curves y² = 4ax and x² = 4ay.