English

The Length of the Perpendicular Drawn from the Point P (3, 4, 5) on Y-axis is

Advertisements
Advertisements

Question

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

Options

  •  10

  • \[\sqrt{34}\] 

     
  •  \[\sqrt{113}\] 

  •  512 

MCQ
Advertisements

Solution

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

\[\sqrt{3^2 + 5^2}\]
\[ = \sqrt{34}\] 

Hence, the correct answer is option (b) 

shaalaa.com
  Is there an error in this question or solution?
Chapter 28: Introduction to three dimensional coordinate geometry - Exercise 28.5 [Page 23]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 28 Introduction to three dimensional coordinate geometry
Exercise 28.5 | Q 13 | Page 23

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Name the octants in which the following points lie:

(1, 2, 3), (4, –2, 3), (4, –2, –5), (4, 2, –5), (–4, 2, –5), (–4, 2, 5),

(–3, –1, 6), (2, –4, –7).


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.


If the origin is the centroid of the triangle PQR with vertices P (2a, 2, 6), Q (–4, 3b, –10) and R (8, 14, 2c), then find the values of a, b and c.


Name the octants in which the following points lie:

(–5, 4, 3) 


Name the octants in which the following points lie: 

(–5, –4, 7) 


Name the octants in which the following points lie: 

(–5, –3, –2) 


Name the octants in which the following points lie: 

(–7, 2 – 5)


Find the image  of: 

 (–5, 0, 3) in the xz-plane. 


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). 


Determine the point on z-axis which is equidistant from the points (1, 5, 7) and (5, 1, –4).


Find the points on z-axis which are at a distance \[\sqrt{21}\]from the point (1, 2, 3). 


Prove that the triangle formed by joining the three points whose coordinates are (1, 2, 3), (2, 3, 1) and (3, 1, 2) is an equilateral triangle.


Find the coordinates of the point which is equidistant  from the four points O(0, 0, 0), A(2, 0, 0), B(0, 3, 0) and C(0, 0, 8).


Are the points A(3, 6, 9), B(10, 20, 30) and C(25, –41, 5), the vertices of a right-angled triangle?


Verify the following: 

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


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


Show that the points A(1, 2, 3), B(–1, –2, –1), C(2, 3, 2) and D(4, 7, 6) are the vertices of a parallelogram ABCD, but not a rectangle.


Find the ratio in which the sphere x2 + y2 z2 = 504 divides the line joining the points (12, –4, 8) and (27, –9, 18).


Show that the plane ax + by cz + d = 0 divides the line joining the points (x1y1z1) and (x2y2z2) in the ratio \[- \frac{a x_1 + b y_1 + c z_1 + d}{a x_2 + b y_2 + c z_2 + d}\]


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


What is the locus of a point for which y = 0, z = 0?


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


The x-coordinate of a point on the line joining the points Q(2, 2, 1) and R(5, 1, –2) is 4. Find its z-coordinate.


Find the co-ordinates of the foot of perpendicular drawn from the point A(1, 8, 4) to the line joining the points B(0, –1, 3) and C(2, –3, –1).


Find the image of the point having position vector `hati + 3hatj + 4hatk` in the plane `hatr * (2hati - hatj + hatk)` + 3 = 0.


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


Prove that the lines x = py + q, z = ry + s and x = p′y + q′, z = r′y + s′ are perpendicular if pp′ + rr′ + 1 = 0.


Find the equation of a plane which bisects perpendicularly the line joining the points A(2, 3, 4) and B(4, 5, 8) at right angles.


Find the equations of the two lines through the origin which intersect the line `(x - 3)/2 = (y - 3)/1 = z/1` at angles of `pi/3` each.


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


O is the origin and A is (a, b, c). Find the direction cosines of the line OA and the equation of plane through A at right angle to OA.


Two systems of rectangular axis have the same origin. If a plane cuts them at distances a, b, c and a′, b′, c′, respectively, from the origin, prove that

`1/a^2 + 1/b^2 + 1/c^2 = 1/(a"'"^2) + 1/(b"'"^2) + 1/(c"'"^2)`


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.


The direction cosines of the vector `(2hati + 2hatj - hatk)` are ______.


The cartesian equation of the plane `vecr * (hati + hatj - hatk)` is ______.


The unit vector normal to the plane x + 2y +3z – 6 = 0 is `1/sqrt(14)hati + 2/sqrt(14)hatj + 3/sqrt(14)hatk`.


The line `vecr = 2hati - 3hatj - hatk + lambda(hati - hatj + 2hatk)` lies in the plane `vecr.(3hati + hatj - hatk) + 2` = 0.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×