If the planes vec rdot( hat i+ hat j+ h...

If the planes ` vec rdot( hat i+ hat j+ hat k)=q_1, vec rdot( hat i+2a hat j+ hat k)=q_2a n d vec rdot(a hat i+a^2 hat j+ hat k)=q_3` intersect in a line, then the value of `a` is a. `1` b. `1//2` c. `2` d. `0`

Text Solution

AI Generated Solution

Topper's Solved these Questions

THEORY OF EQUATIONS
CENGAGE ENGLISH|Exercise JEE ADVANCED (Numerical Value Type )|1 Videos
THREE-DIMENSIONAL GEOMETRY
CENGAGE ENGLISH|Exercise ARCHIVES INTEGER TYPE|1 Videos

Similar Questions

Explore conceptually related problems

Find the angle between the planes vec rdot(2 hat i- hat j+ hat k)=6a n d vec rdot( hat i+ hat j+2 hat k)=5.

Show that the following planes are at right angle: vec rdot((2 hat i- hat j+ hat k)=5\ a n d\ vec rdot((- hat i- hat j+ hat k)=3.

Find the angle between the plane: vec rdot((2 hat i+3 hat j-6 hat k)=5\ a n d\ vec rdot(( hat i-2 hat j+2 hat k)=9.

Find the angle between the plane: vec rdot((2 hat i- hat j+2 hat k)=6\ a n d\ vec rdot((3 hat i+6 hat j-2 hat k)=9.

The distance between the line vec r=(2 hat i-2 hat j+3 hat k)+lambda( hat i- hat j+4 hat k) and plane vec rdot( hat i+5 hat j+ hat k)=5.

Find vec adot vec b when: vec a= hat j- hat k\ a n d\ vec b=2 hat i+3 hat j-2 hat k

Find vec adot vec b when: vec a= hat i-2 hat j+ hat k\ a n d\ vec b=4 hat i-4 hat j+7 hat k

Find the angle between the plane: vec rdot((2 hat i-3 hat j+4 hat k)=1\ a n d\ vec rdot((- hat i+ hat j)=4 .

Show that the vectors vec a=-2 hat i-2 hat j+4 hat k ,\ vec b=-2 hat i+4 hat j-2 hat k\ a n d\ vec c=4 hat i-2 hat j-2 hat k are coplanar.

If vec a= hat i+ hat j+ hat k ,\ vec b=2 hat i- hat j+3 hat k\ a n d\ vec c= hat i-2 hat j+ hat k find a unit vector parallel to 2 vec a- vec b+3 vec c

CENGAGE ENGLISH-THREE DIMENSIONAL GEOMETRY-All Questions

Find the distance of the z-axis from the image of the point M(2-3,3...
Text Solution
|
A line with direction cosines proportional to 1,-5, a n d-2 meets li...
Text Solution
|
If the planes vec rdot( hat i+ hat j+ hat k)=q1, vec rdot( hat i+2a h...
Text Solution
|
The equation of a line passing through the point vec a parallel to ...
Text Solution
|
A straight line L on the xy-plane bisects the angle between O Xa n dO ...
Text Solution
|
Statement 1: Vector vec c=5 hat i+7 hat j+2 hat k is along the bisect...
Text Solution
|
The equation of the line x+y+z-1=0, 4x+y-2z+2=0 written in the symmetr...
Text Solution
|
The equation of two straight lines are (x-1)/2=(y+3)/1=(z-2)/(-3)a n...
Text Solution
|
Statement 1: Lines vec r= hat i+ hat j- hat k+lambda(3 hat i- hat j)a...
Text Solution
|
Statement 1: Line (x-1)/1=(y-0)/2=(z2)/(-1) lies in the plane 2x-3y-4z...
Text Solution
|
What is the equation of the plane which passes through the z-axis and ...
Text Solution
|
Statement 1: let A( vec i+ vec j+ vec k)a n dB( vec i- vec j+ vec k) b...
Text Solution
|
Statement 1: Let theta be the angle between the line (x-2)/2=(y-1)/(-3...
Text Solution
|
If the volume of tetrahedron A B C D is 1 cubic units, where A(0,1,...
Text Solution
|
A rod of length 2 units whose one ends is (1, 0, -1) and other end to...
Text Solution
|
The equation of the plane which is equally inclined to the lines (x...
Text Solution
|
Which of the following lines lie on the plane x+2y-z+4=0? a. (x-1)...
Text Solution
|
The equations of the plane which passes through (0,0,0) and which i...
Text Solution
|
The x-y plane is rotated about its line of intersection with the y-...
Text Solution
|
Consider the planes 3x-6y+2z+5=0a n d4x-12+3z=3. The plane 67 x-162 y+...
Text Solution
|