The projections of a vector on the three coordinate axis are 6, - 3, 2 respectively. The direction cosines of the vector are

•  6, –3, 2 

• 6/5, -3/5, 2/5

• 6/7, -3/7, 2/7

• -6/7, -3/7, 2/7

C.

6/7, -3/7, 2/7

Projection of a vector on coordinate axis are
x₂-x₁, y₂-y₁, z₂-z₁
x₂-x₁ = 6, y₂-y₁ = -3, z₂-z₁ = 2

A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length x. The maximum area enclosed by the park is

• 3x²/2

• x³/8

• x²/2

• πx²

C.

x²/2

If (a, a2 ) falls inside the angle made by the lines y =x/2, x >0 and y = 3x, x > 0, then a belongs to

• (0,1/2)

• (3, ∞)

• (1/2, 3)

• (-3, -1/2)