English

The angle between the line r→=(5i^-j^-4k^)+λ(2i^-j^+k^) and the plane .→(3i^-4j^-k^) + 5 = 0 is sin-1(5291).

Advertisements
Advertisements

Question

The angle between the line `vecr = (5hati - hatj - 4hatk) + lambda(2hati - hatj + hatk)` and the plane `vec.(3hati - 4hatj - hatk)` + 5 = 0 is `sin^-1(5/(2sqrt(91)))`.

Options

  • True

  • False

MCQ
True or False
Advertisements

Solution

This statement is False.

shaalaa.com
  Is there an error in this question or solution?
Chapter 12: Introduction to Three Dimensional Geometry - Exercise [Page 239]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 11
Chapter 12 Introduction to Three Dimensional Geometry
Exercise | Q 44 | Page 239

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Coordinate planes divide the space into ______ octants.


Three vertices of a parallelogram ABCD are A (3, –1, 2), B (1, 2, –4) and C (–1, 1, 2). Find the coordinates of the fourth vertex.


Name the octants in which the following points lie: 

(4, –3, 5)


Name the octants in which the following points lie: 

 (7, 4, –3)


Name the octants in which the following points lie: 

(–7, 2 – 5)


Planes are drawn parallel to the coordinate planes through the points (3, 0, –1) and (–2, 5, 4). Find the lengths of the edges of the parallelepiped so formed.


Planes are drawn through the points (5, 0, 2) and (3, –2, 5) parallel to the coordinate planes. Find the lengths of the edges of the rectangular parallelepiped so formed. 


The coordinates of a point are (3, –2, 5). Write down the coordinates of seven points such that the absolute values of their coordinates are the same as those of the coordinates of the given point.


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


Show that the points A(3, 3, 3), B(0, 6, 3), C(1, 7, 7) and D(4, 4, 7) are the vertices of a square.


If A(–2, 2, 3) and B(13, –3, 13) are two points.
Find the locus of a point P which moves in such a way the 3PA = 2PB.


Verify the following: 

(0, 7, 10), (–1, 6, 6) and (–4, 9, –6) are vertices of a right-angled triangle.


Find the ratio in which the line segment joining the points (2, 4,5) and (3, −5, 4) is divided by the yz-plane.


Find the point on y-axis which is at a distance of  \[\sqrt{10}\] units from the point (1, 2, 3).


Find the point on x-axis which is equidistant from the points A (3, 2, 2) and B (5, 5, 4).


XOZ-plane divides the join of (2, 3, 1) and (6, 7, 1) in the ratio


The coordinates of the foot of the perpendicular drawn from the point P(3, 4, 5) on the yz- plane are


The perpendicular distance of the point P (6, 7, 8) from xy - plane is


The length of the perpendicular drawn from the point P (3, 4, 5) on y-axis is 


The perpendicular distance of the point P(3, 3,4) from the x-axis is 


The length of the perpendicular drawn from the point P(a, b, c) from z-axis is 


If the direction ratios of a line are 1, 1, 2, find the direction cosines of the line.


If a line makes angles α, β, γ with the positive directions of the coordinate axes, then the value of sin2α + sin2β + sin2γ is ______.


If a line makes an angle of `pi/4` with each of y and z axis, then the angle which it makes with x-axis is ______.


Find the angle between the lines whose direction cosines are given by the equations l + m + n = 0, l2 + m2 – n2 = 0


Find the equations of the line passing through the point (3,0,1) and parallel to the planes x + 2y = 0 and 3y – z = 0.


Find the equation of the plane through the points (2, 1, –1) and (–1, 3, 4), and perpendicular to the plane x – 2y + 4z = 10.


Find the equation of the plane which is perpendicular to the plane 5x + 3y + 6z + 8 = 0 and which contains the line of intersection of the planes x + 2y + 3z – 4 = 0 and 2x + y – z + 5 = 0.


Show that the points `(hati - hatj + 3hatk)` and `3(hati + hatj + hatk)` are equidistant from the plane `vecr * (5hati + 2hatj - 7hatk) + 9` = 0 and lies on opposite side of it.


The area of the quadrilateral ABCD, where A(0, 4, 1), B(2,  3, –1), C(4, 5, 0) and D(2, 6, 2), is equal to ______.


The vector equation of the line `(x - 5)/3 = (y + 4)/7 = (z - 6)/2` is ______.


The vector equation of the line through the points (3, 4, –7) and (1, –1, 6) is ______.


The intercepts made by the plane 2x – 3y + 5z +4 = 0 on the co-ordinate axis are `-2, 4/3, - 4/5`.


The angle between the planes `vecr.(2hati - 3hatj + hatk)` = 1 and `vecr.(hati - hatj)` = 4 is `cos^-1((-5)/sqrt(58))`.


The vector equation of the line `(x - 5)/3 = (y + 4)/7 = (z - 6)/2` is `vecr = (5hati - 4hatj + 6hatk) + lambda(3hati + 7hatj - 2hatk)`.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×