Advertisements
Advertisements
प्रश्न
The coordinates of the foot of the perpendicular drawn from the point P(3, 4, 5) on the yz- plane are
पर्याय
(3, 4, 0)
(0, 4, 5)
(3, 0, 5)
(3, 0, 0)
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).
APPEARS IN
संबंधित प्रश्न
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).
Coordinate planes divide the space into ______ octants.
Name the octants in which the following points lie: (5, 2, 3)
Name the octants in which the following points lie:
(4, –3, 5)
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:
(2, –5, –7)
Find the image of:
(–5, 4, –3) in the xz-plane.
Find the distances of the point P(–4, 3, 5) from the coordinate axes.
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).
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).
Find the locus of P if PA2 + PB2 = 2k2, where A and B are the points (3, 4, 5) and (–1, 3, –7).
Verify the following:
(0, 7, –10), (1, 6, –6) and (4, 9, –6) are vertices of an isosceles triangle.
Find the ratio in which the sphere x2 + y2 + z2 = 504 divides the line joining the points (12, –4, 8) and (27, –9, 18).
Write the distance of the point P (2, 3,5) from the xy-plane.
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 length of the perpendicular drawn from the point P(3, 5, 12) on x-axis.
The ratio in which the line joining the points (a, b, c) and (–a, –c, –b) is divided by the xy-plane is
The perpendicular distance of the point P (6, 7, 8) from xy - plane is
If the direction ratios of a line are 1, 1, 2, find the direction cosines of the line.
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 ______.
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 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
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.
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 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 cartesian equation of the plane `vecr * (hati + hatj - hatk)` is ______.
The intercepts made by the plane 2x – 3y + 5z +4 = 0 on the co-ordinate axis are `-2, 4/3, - 4/5`.
The line `vecr = 2hati - 3hatj - hatk + lambda(hati - hatj + 2hatk)` lies in the plane `vecr.(3hati + hatj - hatk) + 2` = 0.
