`-3(1)/(sqrt(2))+(1)/(sqrt(2))`

Find the direction cosines of a vector vecr which is equally inclined with OX,OY and OZ where O is origin. a) 1,1,1 b) -(4)/(sqrt(3)),-(4)/(sqrt(3)),-(4)/(sqrt(3)) c) pm((1)/(sqrt(3)),(1)/(sqrt(3)),(1)/(sqrt(3))) d) -(1)/(sqrt(2)),-(1)/(sqrt(2)),-(1)/(sqrt(2))

(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2))-(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2))+(1)/(sqrt(2)+1)-(1)/(sqrt(2)-1)

Find the conine of the angle between the lines whose direction cosines are ((1)/(sqrt(3)),(1)/(sqrt(3)),(1)/(sqrt(3)))and((1)/(sqrt(2)),(1)/(sqrt(2)),0) .

Prove that : (1)/(sqrt(2)+1)+ (1)/(sqrt(3)+sqrt(2))+ (1)/(2+sqrt(3))=1

Rationalize the denominator (1)/(sqrt(3)-sqrt(2)), (1)/(3sqrt(2)) ,(3)/(sqrt(8))

the value of 3(1)/(sqrt(2)+1)+(1)/(sqrt(3)+sqrt(2))+(1)/(sqrt(4)+sqrt(3))+.........+(1)/(sqrt(16)+sqrt(15)) is

[(1)/(sqrt(2)+sqrt(3)-sqrt(5))+(1)/(sqrt(2)-sqrt(3)-sqrt(5))] in simplified form equals (a) 0 (b) (1)/(sqrt(2)) (c) 1 (c) sqrt(2)

If theta=pi/3, then the volume of pyramid is 1/(sqrt(3)) (b) 1/(3sqrt(2)) (c) 1/(2sqrt(3)) (d) 1/(sqrt(2))

Rationalise the denominator of the following : (1)/(sqrt(3)-sqrt(2)-1)" "(1)/(sqrt(2)+sqrt(3)+sqrt(10))