English
Tamil Nadu Board of Secondary EducationHSC Science Class 12

Choose the correct alternative: If the distance of the point (1, 1, 1) from the origin is half of its distance from the plane x + y + z + k = 0, then the values of k are - Mathematics

Advertisements
Advertisements

Question

Choose the correct alternative:

If the distance of the point (1, 1, 1) from the origin is half of its distance from the plane x + y + z + k = 0, then the values of k are

Options

  • ± 3

  • ± 6

  • – 3, 9

  • 3, – 9

MCQ
Advertisements

Solution

3, – 9

shaalaa.com
Different Forms of Equation of a Plane
  Is there an error in this question or solution?
Chapter 6: Applications of Vector Algebra - Exercise 6.10 [Page 278]

APPEARS IN

Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 12 TN Board
Chapter 6 Applications of Vector Algebra
Exercise 6.10 | Q 23 | Page 278

RELATED QUESTIONS

Find a parametric form of vector equation of a plane which is at a distance of 7 units from t the origin having 3, – 4, 5 as direction ratios of a normal to it


Find the vector and Cartesian equation of the plane passing through the point with position vector `2hat"i" + 6hat"j" + 3hat"k"` and normal to the vector `hat"i" + 3hat"j" + 5hat"k"`


Find the intercepts cut off by the plane `vec"r"*(6hat"i" + 45hat"j" - 3hat"k")` = 12 on the coordinate axes


If a plane meets the co-ordinate axes at A, B, C such that the centroid of the triangle ABC is the point (u, v, w), find the equation of the plane


Find the parametric form of vector equation, and Cartesian equations of the plane passing through the points (2, 2, 1), (9, 3, 6) and perpendicular to the plane 2x + 6y + 6z = 9


Find the non-parametric form of vector equation and cartesian equation of the plane passing through the point (1, − 2, 4) and perpendicular to the plane x + 2y − 3z = 11 and parallel to the line `(x + 7)/3 = (y + 3)/(-1) = z/1`


Find the parametric vector, non-parametric vector and Cartesian form of the equation of the plane passing through the point (3, 6, – 2), (– 1, – 2, 6) and (6, 4, – 2)


Show that the lines `(x - 2)/1 = (y - 3)/1 = (z - 4)/3` and `(x - 1)/(-3) = (y - 4)/2 = (z - 5)/1` are coplanar. Also, find the plane containing these lines


If the straight lines `(x - 1)/1 - (y - 2)/2 = (z - 3)/"m"^2` and `(x - 3)/5 = (y - 2)/"m"^2 = (z - 1)/2` are coplanar, find the distinct real values of m


If the straight lines `(x - 1)/2 = (y + 1)/lambda = z/2` and `(x + 1)/5 = (y + 1)/2 = z/lambda` are coplanar, find λ and equations of the planes containing these two lines


Choose the correct alternative:

If `vec"a", vec"b", vec"c"` are three unit vectors such that `vec"a"` is perpendicular to `vec"b"`, and is parallel to `vec"c"` then `vec"a" xx (vec"b" xx vec"c")` is equal to


Choose the correct alternative:

The volume of the parallelepiped with its edges represented by the vectors `hat"i" + hat"j", hat"i" + 2hat"j", hat"i" + hat"j" + pihat"k"` is


Choose the correct alternative:

If `vec"a"` and `vec"b"` are unit vectors such that `[vec"a", vec"b", vec"a" xx vec"b"] = 1/4`, are unit vectors such that `vec"a"` nad `vec"b"` is


Choose the correct alternative:

If the volume of the parallelepiped with `vec"a" xx vec"b", vec"b" xx vec"c", vec"c" xx vec"a"` as coterminous edges is 8 cubic units, then the volume of the parallelepiped with `(vec"a" xx vec"b") xx (vec"b" xx vec"c"), (vec"b" xx vec"c") xx (vec"c" xx vec"a")` and `(vec"c" xx vec"a") xx (vec"a" xx vec"b")` as coterminous edges is


Choose the correct alternative:

Consider the vectors  `vec"a", vec"b", vec"c", vec"d"` such that `(vec"a" xx vec"b") xx (vec"c" xx vec"d") = vec0`. Let P1 and P2 be the planes determined by the pairs of vectors `vec"a", vec"b"` and `vec'c", vec"d"` respectively. Then the angle between P1 and P2 is


Choose the correct alternative:

Distance from the origin to the plane 3x – 6y + 2z + 7 = 0 is


Let `(x - 2)/3 = (y + 1)/(-2) = (z + 3)/(-1)` lie on the plane px – qy + z = 5, for p, q ∈ R. The shortest distance of the plane from the origin is ______.


The equation of the plane passing through the point (1, 2, –3) and perpendicular to the planes 3x + y – 2z = 5 and 2x – 5y – z = 7, is ______.


The plane passing through the points (1, 2, 1), (2, 1, 2) and parallel to the line, 2x = 3y, z = 1 also passes through the point ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×