Advertisements
Advertisements
प्रश्न
Let (3, 4, –1) and (–1, 2, 3) be the end points of a diameter of a sphere. Then, the radius of the sphere is equal to
पर्याय
2
3
6
7
Advertisements
उत्तर
3
Suppose d is the diameter of the sphere. Then
\[d^2 = \left( - 1 - 3 \right)^2 + \left( 2 - 4 \right)^2 + \left( 3 + 1 \right)^2 \]
\[ \Rightarrow d^2 = \left( - 4 \right)^2 + \left( - 2 \right)^2 + \left( 4 \right)^2 \]
\[ \Rightarrow d^2 = 16 + 4 + 16\]
\[ \Rightarrow d^2 = 36\]
\[ \Rightarrow d = 6\]
Hence, radius of the sphere is 3 units.
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).
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, 4, 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)
Find the image of:
(–4, 0, 0) in the xy-plane.
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.
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).
Find the points on z-axis which are at a distance \[\sqrt{21}\]from the point (1, 2, 3).
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.
Verify the following:
(0, 7, –10), (1, 6, –6) and (4, 9, –6) are vertices of an isosceles triangle.
Verify the following:
(–1, 2, 1), (1, –2, 5), (4, –7, 8) and (2, –3, 4) are vertices of a parallelogram.
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 (x1, y1, z1) and (x2, y2, z2) in the ratio \[- \frac{a x_1 + b y_1 + c z_1 + d}{a x_2 + b y_2 + c z_2 + d}\]
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 (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 length of the perpendicular drawn from the point P (3, 4, 5) on y-axis is
The length of the perpendicular drawn from the point P(a, b, c) from z-axis is
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.
A plane meets the co-ordinates axis in A, B, C such that the centroid of the ∆ABC is the point (α, β, γ). Show that the equation of the plane is `x/alpha + y/beta + z/γ` = 3
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 α, β, γ with the positive directions of the coordinate axes, then the value of sin2α + sin2β + sin2γ is ______.
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.
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 the directions cosines of a line are k, k, k, then ______.
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 vector equation of the line `(x - 5)/3 = (y + 4)/7 = (z - 6)/2` 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.
