Shaalaa.com | 3 Dimensional Geometry part 19 (Plane through point and normal)
Find the equation of the plane which contains the line of intersection of the planes
and whose intercept on x-axis is equal to that of on y-axis.
Write the vector equation of the plane, passing through the point (a, b, c) and parallel to the plane `vec r.(hati+hatj+hatk)=2`
Find the vector equation of the plane which contains the line of intersection of the planes `vecr (hati+2hatj+3hatk)-4=0` and `vec r (2hati+hatj-hatk)+5=0` which is perpendicular to the plane.`vecr(5hati+3hatj-6hatk)+8=0`
Find the vector equation of the plane passing through three points with position vectors ` hati+hatj-2hatk , 2hati-hatj+hatk and hati+2hatj+hatk` . Also find the coordinates of the point of intersection of this plane and the line `vecr=3hati-hatj-hatk lambda +(2hati-2hatj+hatk)`
Find the vector equation of a plane which is at a distance of 5 units from the origin and its normal vector is `2hati-3hatj+6hatk`
Find the vector and cartesian equations of the plane passing throuh the points (2,5,- 3), (-2, - 3,5) and (5,3,-3). Also, find the point of intersection of this plane with the line passing through points (3, 1, 5) and (–1, –3, –1).