If is a unit vector and then find

Find the value of p, if

Write the direction cosines of a line equally inclined to the three coordinate axes.

The length x of a rectangle is decreasing at the rate of 5 cm/minute, and the width y is increasing at the rate of 4 cm/minute. When x = 8 cm and y = 6 cm, find the rate of change of (a) the perimeter, (b) the area of the rectangle.

OR

Find the intervals in which the function f Given: by f(x) = sin x + cos x, 0 ≤ × ≤ 2π, is strictly increasing or strictly decreasing.

If sin y = x sin(a + y), prove that

OR

If (cos x)^y = (sin y)^x, find