Show that the direction cosines of a vector equally inclined to the axes `O X, OY` and `O Z` are `1/(sqrt3), 1/(sqrt3), 1/(sqrt3)`

Show that the vector overset^^i+overset^^j+overset^^k is equally inclined to the axes OX,OY and OZ.

Prove (2+sqrt3)(2-sqrt3)=1

If the direction cosines of a line are (1/c,1/c,1/c) then a) 0 lt c lt 1 b) c gt 2 c) c= pm sqrt2 d) c= pm sqrt3

Find the greatest term in the expansion of sqrt3 (1 + (1)/(sqrt 3))^(20)

Compute the magnitude of the following vectors. veca=hati+hatj+hatk, vecb=2 hati-7 hatj-3 hatk vecc=1/(sqrt3) hati+1/(sqrt3) hatj-1/(sqrt3) hatk

The distance of the plane x+y+z = 1 from the point (1,1,1) is a)4 units b) 1/sqrt3 units c) 4/sqrt3 units d) 1/(4sqrt3) units

Find the equation of the line passing through (2,2 sqrt3) and inclined with the x -axis at an angle of 75^(circ)

Show that tan 15^@ = 2 - sqrt3

sin 315^@ =……….a) -1/2 b) -1/sqrt2 c) -sqrt3/2 d)1

The equation of the straight line making angles 60^(@),60^(@)and45^(@) with positive direction of the coordinate axes and passing through the point (2,1,-1) is a) sqrt(2)(x-2)=sqrt(2)(y-1)=(z+1) b) (x-2)=sqrt(2)(y-1)=(z+1) c) sqrt(2)(x-2)=(y-1)=(z+1) d) (x-2)=sqrt(2)(y-1)=sqrt(2)(z+1)