Home
Class 12
MATHS
If lines x=y=za n dx=y/2=z/3 and third l...

If lines `x=y=za n dx=y/2=z/3` and third line passing through `(1,1,1)` form a triangle of area `sqrt(6)` units, then the point of intersection of third line with the second line will be a. `(1,2,3)` b. `2,4,6` c. `4/3,6/3,(12)/3` d. none of these

A

`(4/3,8/3,12/3)`

B

(1,2,3)

C

(2,4,6)

D

(3,6,9)

Text Solution

Verified by Experts

The correct Answer is:
C
A(1,1,1) lies on x=y=z. Any point on second line is `(lambda,2lambda,3lambda)`.

`costheta=6/sqrt(42), therefore sintheta=sqrt(6)/sqrt(42)`
Area of `triangleOAB=1/2(OA)(OB)sintheta=sqrt(6)`
`=rArr 1/2(sqrt(3))(sqrt(14)lambda)sqrt(6)/sqrt(42) = sqrt(6) rArr lambda=2`
`therefore B=(2,4,6)`.
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE AND HYPERBOLA

    CENGAGE|Exercise Question Bank|1 Videos

  • EQUATION OF PLANE AND ITS APPLICATIONS -I

    CENGAGE|Exercise DPP 3.3|22 Videos

Similar Questions

Explore conceptually related problems

The projection of the line (x+1)/(-1)=y/2=(z-1)/3 on the plane x-2y+z=6 is the line of intersection of this plane with the plane a. 2x+y+2=0 b. 3x+y-z=2 c. 2x-3y+8z=3 d. none of these

Find the equation of straight line joining the points of intersection of the lines 3x+2y+1=0 and x+y=3 to the intersection of the lines y-x=1 and 2x+y+2=0

The slope of the line joining A and B where A is (-1,2) and B is the point of intersection of the lines 2x+3y=5 and 3x+4y=7 is:

The area of the triangle formed by joining the origin to the point of intersection of the line xsqrt(5)+2y=3sqrt(5) and the circle x^2+y^2=10 is (a)3 (b) 4 (c) 5 (d) 6

Find the point of intersection of the lines (x-1)/(3)=(y-1)/(-1) = z+2’and (x-4)/(2)=y=(z+1)/(3) .

If two vertices of a triangle are (-2,3) and (5,-1) the orthocentre lies at the origin, and the centroid on the line x+y=7 , then the third vertex lies at (a) (7,4) (b) (8,14) (c) (12 ,21) (d) none of these

Find the distance of the point (2, 3, -2) from the point of intersection of the straight line passing through the points A(3, 0, 1) and B(6, 4, 3) with the plane x+y-z=7 .

Find the point of intersection of the lines (x-1)/(2)=(y-2)/(3)=(z-3)/(4) and (x-4)/(5)=(y-1)/(2)=z .

Find the equation of line passing through (-2,4,-5) and is parallel to the line (x+3)/3=(y-4)/5=(z+8)/6 .