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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
विकल्प
2
3
6
7
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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.
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संबंधित प्रश्न
Name the octants in which the following points lie: (5, 2, 3)
Name the octants in which the following points lie:
(7, 4, –3)
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(–5, 4, –3) in the xz-plane.
Find the image of:
(5, 2, –7) in the xy-plane.
Find the point on y-axis which is equidistant from the points (3, 1, 2) and (5, 5, 2).
Show that the points A(3, 3, 3), B(0, 6, 3), C(1, 7, 7) and D(4, 4, 7) are the vertices of a square.
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 a right-angled 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.
Show that the points A(1, 2, 3), B(–1, –2, –1), C(2, 3, 2) and D(4, 7, 6) are the vertices of a parallelogram ABCD, but not a rectangle.
What is the locus of a point for which y = 0, z = 0?
Find the ratio in which the line segment joining the points (2, 4,5) and (3, −5, 4) is divided by the yz-plane.
XOZ-plane divides the join of (2, 3, 1) and (6, 7, 1) in the ratio
The perpendicular distance of the point P (6, 7, 8) from xy - plane is
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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.
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 coordinates of the point where the line through (3, – 4, – 5) and (2, –3, 1) crosses the plane passing through three points (2, 2, 1), (3, 0, 1) and (4, –1, 0)
The coordinates of the foot of the perpendicular drawn from the point (2, 5, 7) on the x-axis are given by ______.
If the line drawn from the point (–2, – 1, – 3) meets a plane at right angle at the point (1, – 3, 3), find the equation of the plane
Find the length and the foot of perpendicular from the point `(1, 3/2, 2)` to the plane 2x – 2y + 4z + 5 = 0.
The sine of the angle between the straight line `(x - 2)/3 = (y - 3)/4 = (z - 4)/5` and the plane 2x – 2y + z = 5 is ______.
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 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 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)))`.
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