The direction ratios of the line `2y+z-5=0=x-3y-6` are proportional to `3,\ 1,\ -2` b. `2,\ -4,\ 1` c. `3/(sqrt(14)),1/(sqrt(14)),(-2)/(sqrt(14))` d. `2/(sqrt(41)),(-4)/(sqrt(41)),1/(sqrt(41))`

If the direction ratios of a line are proportional to ( 1, -3, 2 ) then its direction cosines are 1/(sqrt(14)),-3/(sqrt(14)),2/(sqrt(14)) b. 1/(sqrt(14)),2/(sqrt(14)),3/(sqrt(14)) c. -1/(sqrt(14)),3/(sqrt(14)),2/(sqrt(14)) d. -1/(sqrt(14)),-2/(sqrt(14)),-3/(sqrt(14))

The value of sin(1/4sin^(-1)((sqrt(63))/8)) is (a) 1/(sqrt(2)) (b) 1/(sqrt(3)) (c) 1/(2sqrt(2)) (d) 1/(3sqrt(3))

The direction ratio of the line OP are equal and the length OP=sqrt(3) . Then the coordinates of the point P are (A) (-1,-1,-1) (B) (sqrt(3),sqrt(3),sqrt(3)) (C) (sqrt(2),sqrt(2),sqrt(2)) (D) (2,2,2)

Show that : (1)/(3-2sqrt(2))- (1)/(2sqrt(2)-sqrt(7)) + (1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)-2)=5 .

Direction cosines of a line which passes through the points (1,2,3) and (-3,4,1) is A) (4/(2sqrt6), -2/(2sqrt6), 2/(2sqrt6)) B) (4/(2sqrt6), -2/(2sqrt6), -2/(2sqrt6)) C) (4/(2sqrt6), 4/(2sqrt6), 2/(2sqrt6)) D) (-4/(2sqrt6), 1/(2sqrt6), -2/(2sqrt6))

The unit vector normal to the plane x + 2y +3z-6 =0 is (1)/(sqrt(14)) hati + (2)/(sqrt(14))hatj + (3)/(sqrt(14))hatk.

Which of the following is equal to root(3)(-1) a. (sqrt(3)+sqrt(-1))/2 b. (-sqrt(3)+sqrt(-1))/(sqrt(-4)) c. (sqrt(3)-sqrt(-1))/(sqrt(-4)) d. -sqrt(-1)

The eccentricity of the hyperbola x^2-4y^2=1 is a. (sqrt(3))/2 b. (sqrt(5))/2 c. 2/(sqrt(3)) d. 2/(sqrt(5))

1/(sqrt(9)-\ sqrt(8)) is equal to: (a) 3+2sqrt(2) (b) 1/(3+2sqrt(2)) (c) 3-2sqrt(2) (d) 3/2-\ sqrt(2)

Rationalise the denominator of the following : (a)(2)/(3sqrt(3))" "(b)(sqrt(40))/(sqrt(3))(c )" "(3+sqrt(2))/(4sqrt(2))" "(d)(16)/(sqrt(41)-5)" "(e)(2+sqrt(3))/(2-sqrt(3))