If the direction ratios of a line are `1+lamda, 1-lamda, 2` and the line the makes an angle `60^0` with the y-axis, then `lamda` is (A) `1+sqrt(3)` (B) `2+sqrt(5)` (C) `1-sqrt(3)` (D) `2-sqrt(5)`

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)

Equation of a line which passes through A(2,3) and makes an angle 45^@ with x-axis. If this line meets the line x+y+1=0 at the points P, then distance AP is (A) 2sqrt3 (B) 3 sqrt 2 (C) 5sqrt 2 (D) 2sqrt5

The shortest distance between the line yx=1 and the curve x=y^(2) is (A)(3sqrt(2))/(8) (B) (2sqrt(3))/(8) (C) (3sqrt(2))/(5) (D) (sqrt(3))/(4)

A line makes an angle of 30^@ with the positive direction of X-axis.so the slope of the line is…..a) 1/ 2 b) sqrt 3/ 2 c) 1/ sqrt 3 d) sqrt 3

The abscissas of point Pa n dQ on the curve y=e^x+e^(-x) such that tangents at Pa n dQ make 60^0 with the x-axis are. )a) 1n((sqrt(3)+sqrt(7))/7)a n d1n((sqrt(3)+sqrt(5))/2) (b) 1n((sqrt(3)+sqrt(7))/2) (c) 1n((sqrt(7)-sqrt(3))/2) (d) +-1n((sqrt(3)+sqrt(7))/2)

If the volume of parallelopiped formed by the vectors hati+lamdahatj+hatk,hatj+lamdahatk and lamdahati+hatk is minimum then lamda is equal to (1) -(1)/(sqrt(3)) (2) (1)/(sqrt(3)) (3) sqrt(3) (4) -sqrt(3)

A line makes 30^(@) angle with positive direction of y axis in clockwise direction, then slope of line is : ( 1 ) sqrt(3) ( 2 ) - sqrt(3) ( 3 ) 1/(sqrt3) ( 4 ) - 1/(sqrt3)

If the line (x/2+y/3-1)+lamda(2x+y-1)=0 is parallel to x-axis then lamda=

The direction ratios of a line perpendicular to lines whose direction ratios are 2,1,-3and1,-2,1 are: a) -5,-5,-5 b) (5)/(sqrt(3)),(5)/(sqrt(3)),(5)/(sqrt(3)) c) -(1)/(sqrt(3)),-(1)/(sqrt(3)),-(1)/(sqrt(3)) d) -(1)/(3),-(1)/(3),-(1)/(3)