Advertisements
Advertisements
Question
Name the octants in which the following points lie:
(–5, –3, –2)
Advertisements
Solution
The x-coordinate, the y-coordinate and the z-coordinate of the point (−5, −3, −2) are all negative.
Therefore, this point lies in X'OY'Z' octant
APPEARS IN
RELATED QUESTIONS
The x-axis and y-axis taken together determine a plane known as_______.
Coordinate planes divide the space into ______ octants.
Name the octants in which the following points lie:
(7, 4, –3)
Name the octants in which the following points lie:
(2, –5, –7)
Name the octants in which the following points lie:
(–7, 2 – 5)
Find the image of:
(–2, 3, 4) in the yz-plane.
Find the image of:
(–5, 4, –3) in the xz-plane.
Find the image of:
(5, 2, –7) in the xy-plane.
Find the distances of the point P(–4, 3, 5) from the coordinate axes.
Find the locus of P if PA2 + PB2 = 2k2, where A and B are the points (3, 4, 5) and (–1, 3, –7).
Are the points A(3, 6, 9), B(10, 20, 30) and C(25, –41, 5), the vertices of a right-angled triangle?
Show that the plane ax + by + cz + d = 0 divides the line joining the points (x1, y1, z1) and (x2, y2, z2) in the ratio \[- \frac{a x_1 + b y_1 + c z_1 + d}{a x_2 + b y_2 + c z_2 + d}\]
Write the distance of the point P(3, 4, 5) from z-axis.
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 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).
The ratio in which the line joining (2, 4, 5) and (3, 5, –9) is divided by the yz-plane is
What is the locus of a point for which y = 0, z = 0?
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
Find the direction cosines of the line passing through the points P(2, 3, 5) and Q(–1, 2, 4).
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).
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 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 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 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 through the points (2, 1, –1) and (–1, 3, 4), and perpendicular to the plane x – 2y + 4z = 10.
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
The locus represented by xy + yz = 0 is ______.
The plane 2x – 3y + 6z – 11 = 0 makes an angle sin–1(α) with x-axis. The value of α is equal to ______.
The direction cosines of the vector `(2hati + 2hatj - hatk)` are ______.
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))`.
