A line having direction ratios `3, 4, 5` cuts 2 planes `2x - 3y + 6z - 12 = 0` and `2x - 3y + 6z + 2 = 0` at point ` P` & `Q`, then find length of `PQ` (A) `(35sqrt2)/12` (B) `(35sqrt2)/24` (C) `(35sqrt2)/6` (D) `(35sqrt2)/8`

A line having direction ratios 3,4,5 cuts 2 planes 2x-3y+6z-12=0 and 2x-3y+6z+2=0 at point P o* Q, then find length of PQ(A)(35sqrt(2))/(12) (B) (35sqrt(2))/(24) (C) (35sqrt(2))/(6) (D) (35sqrt(2))/(8)

A line having direction ratios 1,2,2 cut two planes 3x-2y+6z+12=0,3x-2y+6z-2=0 at P and Q respectively. If PQ is lambda then [2lambda] =

int_0^3 x(3-x)^(3/2) dx= (A) (108sqrt(3))/35 (B) -(108sqrt(3))/35 (C) (54sqrt(3))/35 (D) none of these

int_0^3 x(3-x)^(3/2) dx= (A) (108sqrt(3))/35 (B) -(108sqrt(3))/35 (C) (54sqrt(3))/35 (D) none of these

A line with positive direction cosines passes through the ont P(2,-1,2) and makes equal angles with the coordinate axes. The line meets the plane 2x+y+z=9 at Q. The length of the line segment PQ equals (A) 1 (B) sqrt(2) (C) sqrt(3) (D) 2

Distance between the lines 5x+3y-7=0\ a n d\ 15 x+9y+14=0 is (35)/(sqrt(34)) b. 1/(3sqrt(34)) c. (35)/(3sqrt(34)) d. 35//2sqrt(34)

Distance between the lines 5x+3y-7=0\ a n d\ 15 x+9y+14=0 is (35)/(sqrt(34)) b. 1/(3sqrt(34)) c. (35)/(3sqrt(34)) d. 35//2sqrt(34)

The point P(x,y,z) lies in the first octant and its distance from the origin is 12 units. If the positon vector of P makes 45^0 and 60^0 with the x-axis and y-axis respectively, then the coordinastes of P are (A) (3sqrt(3),6,3sqrt(2)) (B) (4sqrt(3),8,4sqrt(2)) (C) (6sqrt(2),6,6) (D) (6,6,6sqrt(2))

(sqrt(7)+sqrt(5))/(sqrt(5)) is equal to (a) 1 (b) 2(c)6-sqrt(35) (d) 6+sqrt(35)