English

The distance of the plane r→⋅(24i^+37j^-67k^) = 1 from the origin is ______.

Advertisements
Advertisements

Question

The distance of the plane `vecr * (2/4 hati + 3/7 hatj - 6/7hatk)` = 1 from the origin is ______.

Options

  • 1

  • 7

  • `1/7`

  • None of these

MCQ
Fill in the Blanks
Advertisements

Solution

The distance of the plane `vecr * (2/4 hati + 3/7 hatj - 6/7hatk)` = 1 from the origin is 1.

Explanation:

The given equation is of the form `vecr * hatn = p` 

Where `hatn` is a unit vector and p > 0

i.e., in the normal form.

shaalaa.com
  Is there an error in this question or solution?
Chapter 12: Introduction to Three Dimensional Geometry - Exercise [Page 238]

APPEARS IN

NCERT Exemplar Mathematics Exemplar [English] Class 11
Chapter 12 Introduction to Three Dimensional Geometry
Exercise | Q 31 | Page 238

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Find the distance between the following pairs of points:

(–3, 7, 2) and (2, 4, –1)


Find the distance between the following pairs of points:

(2, –1, 3) and (–2, 1, 3)


Verify the following:

(0, 7, –10), (1, 6, –6) and (4, 9, –6) are the vertices of an isosceles triangle.


Verify the following:

(–1, 2, 1), (1, –2, 5), (4, –7, 8) and (2, –3, 4) are the vertices of a parallelogram.


Find the equation of the set of points which are equidistant from the points (1, 2, 3) and (3, 2, –1).


Find the equation of the set of points P, the sum of whose distances from A (4, 0, 0) and B (–4, 0, 0) is equal to 10.


Find the distance between the following pairs of points: 

P(1, –1, 0) and Q(2, 1, 2)


Find the distance between the following pairs of point: 

A(3, 2, –1) and B(–1, –1, –1).


Find the distance between the points P and Q having coordinates (–2, 3, 1) and (2, 1, 2).


Using distance formula prove that the following points are collinear:

A(4, –3, –1), B(5, –7, 6) and C(3, 1, –8)


Using distance formula prove that the following points are collinear: 

P(0, 7, –7), Q(1, 4, –5) and R(–1, 10, –9)


Using distance formula prove that the following points are collinear: 

A(3, –5, 1), B(–1, 0, 8) and C(7, –10, –6)


Determine the points in xy-plan are equidistant from the points A(1, –1, 0), B(2, 1, 2) and C(3, 2, –1).


Show that the points (0, 7, 10), (–1, 6, 6) and (–4, 9, 6) are the vertices of an isosceles right-angled triangle. 


Write the coordinates of third vertex of a triangle having centroid at the origin and two vertices at (3, −5, 7) and (3, 0, 1). 


Find the distance of the point whose position vector is `(2hati + hatj - hatk)` from the plane `vecr * (hati - 2hatj + 4hatk)` = 9


Find the distance of the point (– 2, 4, – 5) from the line `(x + 3)/3 = (y - 4)/5 = (z + 8)/6`


Find the distance of the point (–1, –5, – 10) from the point of intersection of the line `vecr = 2hati - hatj + 2hatk + lambda(3hati + 4hatj + 2hatk)` and the plane `vecr * (hati - hatj + hatk)` = 5.


The distance of a point P(a, b, c) from x-axis is ______.


Find the angle between the lines `vecr = 3hati - 2hatj + 6hatk + lambda(2hati + hatj + 2hatk)` and `vecr = (2hatj - 5hatk) + mu(6hati + 3hatj + 2hatk)`


Find the equation of a plane which is at a distance `3sqrt(3)` units from origin and the normal to which is equally inclined to coordinate axis


Find the distance of a point (2, 4, –1) from the line `(x + 5)/1 = (y + 3)/4 = (z - 6)/(-9)`


Find the equation of the plane through the intersection of the planes `vecr * (hati + 3hatj) - 6` = 0 and `vecr * (3hati + hatj + 4hatk)` = 0, whose perpendicular distance from origin is unity.


The points A(5, –1, 1); B(7, –4, 7); C(1, –6, 10) and D(–1, –3, 4) are vertices of a ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×