The direction cosines of the ray from `(0,0,0) to (2,-3,6)` are (A) `-2/7,3/7,-6/7` (B) `2/7,37,6/7` (C) `-2/7,-3/7,6/7` (D) `2/7,-3/7,6/`

The direction cosines of a normal to the plane 2x-3y-6z+14=0 are (A) (2/7,(-3)/7,(-6)/7) (B) ((-2)/7,3/7,6/7) (C) ((-2)/7,(-3)/3,(-6)/7) (D) none of these

The projections of a vector on the three coordinate axis are 6, 3, 2 respectively. The direction cosines of the vector are (A) 6,-3,2 (B) 6/5,(-3)/5,2/5 (C) 6/7,(-3)/7,2/7 (D) (-6)/7,(-3)/7,2/7

If projections of as line on x,y and z axes are 6,2 and 3 respectively, then directions cosines of the lines are (A) (6/2,2/7,3/7) (B) (3/5,5/7,6/7) (C) (1/7,2/7,3/7) (D) none of these

The inverse of the matrix [(2,3),(-4,7)] is (A) [(-2,-3),(4,-7)] (B) 1/26 [(7,-3),(4,2)] (C) [(7,4),(-3,2)] (D) [(7,-3),(4,2)]

The three roots of the equation |[x,3,7],[2,x,2],[7,6,x]| =0 are

The slope of the tangent to the curve x=t^2+3t-8, y=2t^2-2t-5 at the point (2, -1) is(A) (22)/7 (B) 6/7 (C) 7/6 (D) (-6)/7

O is origin and P is a point at a distance of 7 units from origin if the direction ratios of OP are lt 3 ,-2, 6 gt , then the coordinates of P are (i) (3,-2,6) (ii) (21,-14,42) (iii) (3/7,-2/7,6/7) (iv) none of these

A point on the line (x-1)/1=(y-2)/2=(z+1)/3 at a distance sqrt(6) from the origin is (A) ((-5)/7, (-10)/7,13/7) (B) (5/7,10/7,(-13)/7) (C) (1,2,-1) (D) (-1,-2,1)

The centre of a circle whose end points of a diameter are (-6,3) and (6,4) a) (8,-1) b) (4,7) c) (0, 7/2 ) d) (4, 7/2 )

The centre of a circle whose end points of a diameter are (-6,3) and (6,4) a) (8,-1) b) (4,7) c) (0, 7/2 ) d) (4, 7/2 )