Home
Class 12
MATHS
The equation of the straight line throug...

The equation of the straight line through the origin and parallel to the line `(b+c)x+(c+a)y+(a+b)z=k=(b-c)x+(c-a)y+(a-b)z` are

A

`(x)/(b^2-c^2)=(y)/(c^2-a^2)=(z)/(a^2-b^2)`

B

`(x)/(b)=(y)/(b)=(z)/(a)`

C

`(x)/(a^2-bc)=(y)/(b^2-ca)=(z)/(c^2-ab)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
(c)
Promotional Banner

Similar Questions

Explore conceptually related problems

Prove that the line through the point (x_1, y_1) and parallel to the line Ax + By + C=0 is A(x-x_1) + B(y-y_1)=0 .

Find the equation of the tangent line to the curve y = x^(2) – 2x +7 which is (a) parallel to the line 2x – y + 9 = 0 (b) perpendicular to the line 5y – 15x = 13.

The equation of the plane passing through the line of intersection of the planes 2x + y -z=1 and 2x + 2y -z = 1/2 and also passing through the origin is ..............

In each of the following cases, determine the direction cosines of the normal to the plane and the distance from the origin. (a) z=2 (b) x+y+z=1 (c) 2x+3y-z=5 (b) 5y+8=0

Prove that the straight lines joining the origin to the point of intersection of the straight line h x+k y=2h k and the curve (x-k)^2+(y-h)^2=c^2 are perpendicular to each other if h^2+k^2=c^2dot

A point P moves on a plane (x)/(a)+(y)/(b)+(z)/(c)=1 . A plane through P and perpendicular to OP meets the coordinate axes in A, B and C. If the planes throught A, B and C parallel to the planes x=0, y=0 and z=0 intersect in Q, then find the locus of Q.

If the foot of perpendicular drawn from the point (a,b,c) and the line x = y = z then .....

Find the angle between the lines whose direction ratios are a, b, c and b-C, c-a, a-b.

Two different non-parallel lines meet the circle abs(z)=r . One of them at points a and b and the other which is tangent to the circle at c. Show that the point of intersection of two lines is (2c^(-1)-a^(-1)-b^(-1))/(c^(-2)-a^(-1)b^(-1)) .

If vec xa n d vec y are two non-collinear vectors and a, b, and c represent the sides of a A B C satisfying (a-b) vec x+(b-c) vec y+(c-a)( vec x X vec y)=0, then A B C is (where vec x X vec y is perpendicular to the plane of xa n dy ) a. an acute-angled triangle b. an obtuse-angled triangle c. a right-angled triangle d. a scalene triangle