The line segment joining the points A,B makes projection `1,4,3 on x,y,z` axes respectively then the direction cosiners of AB are (A) 1,4,3 (B) `1/sqrt(26),4/sqrt(26),3/sqrt(26)` (C) `(-1)/sqrt(26, 4/sqrt(26),3/sqrt(26)` (D) `1/sqrt(26),(-4)/sqrt(26),3/(sqrt(26)`

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 |{:(sqrt(13 )+ sqrt(3), 2sqrt(5),sqrt(5)),(sqrt(15) + sqrt(26),5,sqrt(10)),(3 + sqrt(65), sqrt(15),5):}|

Find the angle between the lines whose direction cosines are (-(sqrt3)/(4), (1)/(4), -(sqrt3)/(2)) and (-(sqrt3)/(4), (1)/(4), (sqrt3)/(2)) .

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 sum of the series (1)/(sqrt(1)+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+ . . . . .+(1)/(sqrt(n^(2)-1)+sqrt(n^(2))) equals

For all n in N, 1 + 1/(sqrt(2))+1/(sqrt(3))+1/(sqrt(4))++1/(sqrt(n))

sin( 67 1/2)^(@) + cos( 67 1/2)^(@) is equal to A) 1/2sqrt(4+2sqrt(2)) , B) 1/2sqrt(4-2sqrt(2)) , C) 1/4(sqrt(4+2sqrt(2))) , D) 1/4(sqrt(4-2sqrt(2)))

Find the value of determinant |sqrt((13))+sqrt(3)2sqrt(5)sqrt(5)sqrt((15))+sqrt((26))5sqrt((10))3+sqrt((65))sqrt((15))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))

Length of E F is equal to- a. 1+sqrt(3)-sqrt(6) b. \ 1+sqrt(3)-sqrt(2) c. \ sqrt(6)-1-sqrt(3) d. sqrt(2)-1+sqrt(3)