Find the Cartesian as well as vector equ...

Find the Cartesian as well as vector equations of the planes through the intersection of the planes ` vec rdot((2 hat i+6 hat j)+12=0\ a n d\ vec rdot((3 hat i- hat j-4 hat k)=0` which are at a unit distance from the origin.

Text Solution

AI Generated Solution

Topper's Solved these Questions

TANGENTS AND NORMALS
RD SHARMA ENGLISH|Exercise All Questions|244 Videos
VECTOR OR CROSS PRODUCT
RD SHARMA ENGLISH|Exercise All Questions|147 Videos

Similar Questions

Explore conceptually related problems

Find the equation of the plane through the line of intersection of the planes vec rdot(( hat i+3 hat j)+6=0\ a n d\ vec rdot((3 hat i- hat j-4 hat k)=0, which is at a unit distance from the origin.

Find the equation of the plane passing through the intersection of the planes vec rdot( (hat i+ hat j+ hat k)=1\ a n d\ vec rdot((2 hat i+3 hat j- hat k)+4=0 and parallel to x-axis.

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.

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

Find the equation of a plane through the intersection of the planes vec rdot( hat i+3 hat j- hat k)=5a n d vec rdot(2 hat i- hat j+ hat k)=3 and passing through the point (2,1,-2)dot

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 .

Find the vector equation of the line passing through (1,2,3) and parallel to the planes vec rdot( hat i- hat j+2 hat k)a n d vec rdot(3 hat i+ hat j+ hat k)=6.

Find the vector equation of the line passing through (1, 2, 3 ) and parallel to the planes vec rdot( (hat i- hat j+2 hat k)=5\ a n d\ vec rdot((3 hat i+ hat j+ hat k)=6.

Find the vector equation of the plane passing through the intersection of the planes -> rdot( hat i+ hat j+ hat k)=6 and -> rdot(2 hat i+3 hat j+4 hat k)=-5 and the point (1, 1, 1).

RD SHARMA ENGLISH-THE PLANE -All Questions

Find the equation of a plane containing the line of intersection of...
Text Solution
|
Direction ratios of the normal to the plane passing through the points...
Text Solution
|
Find the Cartesian as well as vector equations of the planes through ...
Text Solution
|
Find the equation of the plane which is parallel to 2x-3y+z=0 and whic...
Text Solution
|
Find the equation of the plane through (3, 4, -1) which is parallel to...
Text Solution
|
Find the equation of the plane passing through the line of intersectio...
Text Solution
|
Find the equation of the plane through the point 2 hat i+ hat j- hat k...
Text Solution
|
Find dy/dx if 4x+5y=8
Text Solution
|
Find the equation of the plane through the line of intersection of the...
Text Solution
|
Find the vector equation (in scalar product form) of the plane cont...
Text Solution
|
Find the equation of the plane which is perpendicular to the plane 5x+...
Text Solution
|
Find the equation of the plane through the line of intersection of the...
Text Solution
|
Find the equation of the plane through the intersection of the planes ...
Text Solution
|
Find the equation of the plane through the line of intersection of the...
Text Solution
|
Prove that if a plane has the intercepts a, b, c and is at a distance...
Text Solution
|
If the points (1,\ 1,\ lambda)a n d\ (-3,\ 0,\ 1) be equidistant from ...
Text Solution
|
Find the distance between the point P(6, 5, 9)and the plane determine...
Text Solution
|
Find the equation of a plane passing through the point P(6,\ 5,\ 9) an...
Text Solution
|
A variable plane is at a constant distance p from the origin and meets...
Text Solution
|
A variable plane at a constant distance p from the origin meets the co...
Text Solution
|