हिंदी

The Coordinates of the Foot of the Perpendicular Drawn from the Point P(3, 4, 5) on The Yz- Plane Are - Mathematics

Advertisements
Advertisements

प्रश्न

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

विकल्प

  • (3, 4, 0)

  •  (0, 4, 5) 

  • (3, 0, 5) 

  •  (3, 0, 0) 

MCQ
Advertisements

उत्तर

We know that the x - coordinate on yz - plane is 0.
The coordinates of the foot of the perpendicular drawn from the point P(3, 4, 5) on the yz- plane are (0, 4, 5).
Hence, the correct answer is option (b).

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 28: Introduction to three dimensional coordinate geometry - Exercise 28.5 [पृष्ठ २३]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 28 Introduction to three dimensional coordinate geometry
Exercise 28.5 | Q 10 | पृष्ठ २३

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Name the octants in which the following points lie: 

 (7, 4, –3)


Name the octants in which the following points lie: 

(–5, –4, 7) 


Name the octants in which the following points lie:

 (2, –5, –7) 


A cube of side 5 has one vertex at the point (1, 0, –1), and the three edges from this vertex are, respectively, parallel to the negative x and y axes and positive z-axis. Find the coordinates of the other vertices of the cube.


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.


Find the distances of the point P(–4, 3, 5) from the coordinate axes. 


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


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.


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.


Show that the points (a, b, c), (b, c, a) and (c, a, b) are the vertices of an equilateral triangle. 


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 an isosceles triangle.


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.


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 \[- \frac{a x_1 + b y_1 + c z_1 + d}{a x_2 + b y_2 + c z_2 + d}\]


The coordinates of the mid-points of sides AB, BC and CA of  △ABC are D(1, 2, −3), E(3, 0,1) and F(−1, 1, −4) respectively. Write the coordinates of its centroid.


Write the coordinates of the foot of the perpendicular from the point (1, 2, 3) on y-axis.


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


The ratio in which the line joining the points (a, b, c) and (–a, –c, –b) is divided by the xy-plane is


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


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


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


If α, β, γ are the angles that a line makes with the positive direction of x, y, z axis, respectively, then the direction cosines of the line are ______.


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


If a variable line in two adjacent positions has direction cosines l, m, n and l + δl, m + δm, n + δn, show that the small angle δθ between the two positions is given by δθ2 = δl2 + δm2 + δn2


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.


Find the foot of perpendicular from the point (2,3,–8) to the line `(4 - x)/2 = y/6 = (1 - z)/3`. Also, find the perpendicular distance from the given point to the line.


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 straight lines whose direction cosines are given by 2l + 2m – n = 0 and mn + nl + lm = 0 are at right angles.


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


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)))`.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×