मराठी

The Length of the Perpendicular Drawn from the Point P(A, B, C) from Z-axis is - Mathematics

Advertisements
Advertisements

प्रश्न

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

पर्याय

  • \[\sqrt{a^2 + b^2}\] 

  • \[\sqrt{b^2 + c^2}\] 

  • \[\sqrt{a^2 + c^2}\]

  •  \[\sqrt{a^2 + b^2 + c^2}\]

MCQ
Advertisements

उत्तर

The length of the perpendicular drawn from the point P(x, y, z) from z-axis is given by \[\sqrt{y^2 + x^2}\] Thus, the length of the perpendicular drawn from the point P(a, b, c) from z-axis is \[\sqrt{a^2 + b^2}\] 

Hence, the correct answer is option (a)

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 28: Introduction to three dimensional coordinate geometry - Exercise 28.5 [पृष्ठ २३]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
पाठ 28 Introduction to three dimensional coordinate geometry
Exercise 28.5 | Q 15 | पृष्ठ २३

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

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: (5, 2, 3)


Name the octants in which the following points lie: 

(–5, –3, –2) 


Find the image  of:

 (5, 2, –7) in the xy-plane.


Find the image  of: 

 (–5, 0, 3) in the xz-plane. 


Find the image  of: 

 (–4, 0, 0) in the xy-plane. 


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. 


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


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.


Prove that the point A(1, 3, 0), B(–5, 5, 2), C(–9, –1, 2) and D(–3, –3, 0) taken in order are the vertices of a parallelogram. Also, show that ABCD is not a rectangle.


Verify the following: 

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


Verify the following:

 (5, –1, 1), (7, –4,7), (1, –6,10) and (–1, – 3,4) are the vertices of a rhombus.


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


Find the equation of the set of the points P such that its distances from the points A(3, 4, –5) and B(–2, 1, 4) are equal.


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


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(3, 3,4) from the x-axis is 


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


If a line makes an angle of 30°, 60°, 90° with the positive direction of x, y, z-axes, respectively, then find its direction cosines.


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


A line makes equal angles with co-ordinate axis. Direction cosines of this line are ______.


If a line makes angles `pi/2, 3/4 pi` and `pi/4` with x, y, z axis, respectively, then its direction cosines are ______.


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


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


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 length and the foot of perpendicular from the point `(1, 3/2, 2)` to the plane 2x – 2y + 4z + 5 = 0.


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.


The plane ax + by = 0 is rotated about its line of intersection with the plane z = 0 through an angle α. Prove that the equation of the plane in its new position is ax + by `+- (sqrt(a^2 + b^2) tan alpha)z ` = 0


If l1, m1, n1 ; l2, m2, n2 ; l3, m3, n3 are the direction cosines of three mutually perpendicular lines, prove that the line whose direction cosines are proportional to l1 + l2 + l3, m1 + m2 + m3, n1 + n2 + n3 makes equal angles with them.


The locus represented by xy + yz = 0 is ______.


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


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


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


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


If the foot of perpendicular drawn from the origin to a plane is (5, – 3, – 2), then the equation of plane is `vecr.(5hati - 3hatj - 2hatk)` = 38.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×