Home
Class 12
MATHS
Consider the lines L1 : r=a+lambdab and ...

Consider the lines `L_1 : r=a+lambdab and L_2 : r=b+mua`, where a and b are non zero and non collinear vectors.
Statement-I `L_1 and L_2` are coplanar and the plane containing these lines passes through origin.
Statement-II `(a-b)cdot(atimesb)=0` and the plane containing `L_1 and L_2` is [r a b]=0 which passe through origin.

A

Statement-I is true, Statement II is also true, Statement-II is the correct explanation of Statement-I.

B

Statement-I is true, Statement-II is also true, Statement-II is not the correct explanation of Statement-I.

C

Statement-I is true, Statement-II is false.

D

Statement-I is false, Statement -II is true.

Text Solution

Verified by Experts

The correct Answer is:
(a)
Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|35 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Three Dimensional Coordinate System Exercise 9 : Match Type Questions|7 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|28 Videos

  • THEORY OF EQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|35 Videos

  • TRIGONOMETRIC EQUATIONS AND INEQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

Similar Questions

Explore conceptually related problems

Equations of the line which passe through the point with position vector (2, 1, 0) and perpendicular to the plane containing the vectors i+j and j+k is

Find the direction cosines of the unit vector perpendicular to the plane vecr cdot(6hati-3hatj-2hatk) +1 = 0 passing through the origin.

Consider the lines : L_1: (x-7)/3=(y-7)/2=(z-3)/1 and L_2: (x-1)/2=(y+1)/4=(z+1)/3 . If a line 'L' whose direction ratios are intersects the lines L_1 and L_2 at A and B respectively, then the distance of (AB)/2 is:

Find the vector quation of the plane containing the line of intersection of the planes x-3y+4z-5=0 and 2x-y+3z-1=0 and passing through the point (1,-2,3).

Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane vecr cdot(hati+2hatj-5hatk) + 9 = 0

Show that the relation R defined in the set A of all lines as R = {(L_1, L_2): L_1 and L_2 are parallel lines} is an equivalence relation.

Consider the line L 1 : x +1/3 = y+ 2/1= z +1/2 L2 : x-2/1= y+2/2= z-3/3 The unit vector perpendicular to both L 1 and L 2 lines is

A(-2, 2, 3) and B(13, -3, 13) and L is a line through A. Q. Equation of a line L, perpendicular to the line AB is

Line L has intercepts a and b on the coordinate axes. When the axes are rotated through a given angle keeping the origin fixed, the same line L has intercepts p and q . Then

A line L_1 passes through the point 3i and parallel to the vector − i + j + k and another line L_2 passes through the point i + j and parallel to the vector i + k then point of intersection of the lines is