Question
Find the radius and the center of the circular section of the sphere |r| = 26 cut off by the plane r . (2i+6j+3k) = 70.
Answer :
Word Count : 531
___ ___ _______ ____ ________ ____ ___.
___ __________ ___ _________ ________.
_________ _____ ____ __________ __________ _________ __________.
_________ ________ _________ _______ ______ _________ _______ ________ ____ _____ ______ _________.
_________ _______ _______ ___ ________ ________.
______ ____ _____ _________ ____ __________ _____ ____ ________ _______.
_____ ___ ___ _________ ________ _________.
___ __________ _________ ___ ________ _________ _________ ________ ______ _________ _______.
_____ _____ __________ _______ _____ ___ ______ ___ ____ ______.
_________ _________ __________ ___ __________ __________ ______ __________ _________ ____.
_________ _____ _______ ________ ______ _________ __________ ___ _______.
________ _____ ______ ______ _________ ____ _______ ______ ______ ______ __________ ___.
__________ ____ ________ _____ ______ ___ __________ ___.
___ ____ __________ __________ _________ _____ __________ _________.
_________ __________ _________ ___ _______ _____.
________ ___ ________ ______ _________ ___ ______.
_______ __________ _______ ________ __________.
_____ ___ ______ ______ ________ _______ _______ __________ ___ ___.
________ ________ _______ ____ _____ ______ __________ ________ ____ ________ _____ _______.
____ ___ _______ ___ _____ ___ __________ ___ __________ _____ ______ ___.
________ ______ _______ ________ ________ _____ _______.
___ _____ __________ ____ _____ ___.
_______ ______ _________ __________ ___ ____ ___ ___ ____ _____.
____ ____ ____ ________ ________ ________ ____ _____ ___ ____ ___.
_________ ______ ________ __________ __________ ___ ____ ___ ______ ___ _______ __________.
____ ___ __________ ________ ________ _____ _________ ___ ______ ______ ____.
_________ __________ _____ _____ _______ ________ _____ _________ ____ ________ _______ ___.
______ ___ __________ _________ __________ _____ _______ _________ ___ ____ ____ _________.
______ _________ ___ _________ ________.
________ ______ _____ _________ _____ ____ ___ ________ __________ _________.
_______ _______ __________ ______ _________ _________ ____ ____ __________.
__________ ______ ______ _______ _____ ____.
______ ________ ___ _____ ______ _____ ___ _________ ___ _________.
_____ _________ _______ ______ ________ ______ ______ ________ _____.
_________ _________ ____ _________ __________ ______ _____ ________ ________ ________.
______ _______ ___ _______ ________ __________ _______ _________ _____ ___.
____ _________ ____ _________ __________ ______ ________ ________ _______ ________.
_____ _________ _________ ______ ____ ________ _______ ____.
__________ __________ _____ _____ ______.
___ _______ __________ ______ ____ ________ _____ ____ ______ _____ ________.
________ ________ _____ __________ _____ _____ __________ ___ ________ ___.
_____ ____ _________ __________ ____ _______ _____ ______ _______.
____ ______.
Skip in 10
To solve the problem, we need to find the radius and the center of the circular section of a sphere that is cut off by a plane. Given: - The sphere equation: \(|r| = 26\), which means the radius of the sphere is 26. - The equation of the plane: \(r \cdot (2\hat{i} + 6\hat{j} + 3\hat{k}) = 70\). ### Step 1: Sphere Equation The equation of the sphere is: \[ x^2 + y^2 + z^2 = 26^2 = 676. \] This represents a sphere with center at the origin \((0, 0, 0)\) and radius 26. ### Step 2: Plane Equation The plane is given by: \[ r \cdot (2\hat{i} + 6\hat{j} + 3\hat{k}) = 70, \] which can be written as: \[ 2x + 6y + 3z = 70. \] This is a plane with normal vector \(\vec{n} = (2, 6, 3)\).
_______ _______ ___ __________ _______ ________ ____ _____ __________ ______.___ ___ _______ ____ ________ ____ ___.
___ __________ ___ _________ ________.
_________ _____ ____ __________ __________ _________ __________.
_________ ________ _________ _______ ______ _________ _______ ________ ____ _____ ______ _________.
_________ _______ _______ ___ ________ ________.
______ ____ _____ _________ ____ __________ _____ ____ ________ _______.
_____ ___ ___ _________ ________ _________.
___ __________ _________ ___ ________ _________ _________ ________ ______ _________ _______.
_____ _____ __________ _______ _____ ___ ______ ___ ____ ______.
_________ _________ __________ ___ __________ __________ ______ __________ _________ ____.
_________ _____ _______ ________ ______ _________ __________ ___ _______.
________ _____ ______ ______ _________ ____ _______ ______ ______ ______ __________ ___.
__________ ____ ________ _____ ______ ___ __________ ___.
___ ____ __________ __________ _________ _____ __________ _________.
_________ __________ _________ ___ _______ _____.
________ ___ ________ ______ _________ ___ ______.
_______ __________ _______ ________ __________.
_____ ___ ______ ______ ________ _______ _______ __________ ___ ___.
________ ________ _______ ____ _____ ______ __________ ________ ____ ________ _____ _______.
____ ___ _______ ___ _____ ___ __________ ___ __________ _____ ______ ___.
________ ______ _______ ________ ________ _____ _______.
___ _____ __________ ____ _____ ___.
_______ ______ _________ __________ ___ ____ ___ ___ ____ _____.
____ ____ ____ ________ ________ ________ ____ _____ ___ ____ ___.
_________ ______ ________ __________ __________ ___ ____ ___ ______ ___ _______ __________.
____ ___ __________ ________ ________ _____ _________ ___ ______ ______ ____.
_________ __________ _____ _____ _______ ________ _____ _________ ____ ________ _______ ___.
______ ___ __________ _________ __________ _____ _______ _________ ___ ____ ____ _________.
______ _________ ___ _________ ________.
________ ______ _____ _________ _____ ____ ___ ________ __________ _________.
_______ _______ __________ ______ _________ _________ ____ ____ __________.
__________ ______ ______ _______ _____ ____.
______ ________ ___ _____ ______ _____ ___ _________ ___ _________.
_____ _________ _______ ______ ________ ______ ______ ________ _____.
_________ _________ ____ _________ __________ ______ _____ ________ ________ ________.
______ _______ ___ _______ ________ __________ _______ _________ _____ ___.
____ _________ ____ _________ __________ ______ ________ ________ _______ ________.
_____ _________ _________ ______ ____ ________ _______ ____.
__________ __________ _____ _____ ______.
___ _______ __________ ______ ____ ________ _____ ____ ______ _____ ________.
________ ________ _____ __________ _____ _____ __________ ___ ________ ___.
_____ ____ _________ __________ ____ _______ _____ ______ _______.
____ ______.
IGNOU ACADEMY
Your IGNOU journey, made easier.
- Solved Assignments
- Study Notes
- Guess Papers
- Question Papers
Continue Reading — It's Free
Sign in with Google to unlock more of this answer.
✓ Free access
✓ Unlock up to 60% of the answer
✓ No payment required
✓ Unlock up to 60% of the answer
✓ No payment required
Quick Google sign-in. No separate registration form.
Related Questions
Reduce the conic x2+6xy+y2 - 8 = 0 to standard form. Hence identify the given conic.
Define T : R3 → R3 by
T (x, y, x) = (x + y, y, 2x − 2y + 2z).
Check that T satisfies the polynomial (x − 1)2(x − 2). Find the minimal polynomial of T .
Complete the set S = {x3+x2+1,x2+x+1,x+1} to get a basis of P3
Find the inverse of the matrix
using row reduction.
Find the radius and the center of the circular section of the sphere |r| = 26 cut off by the plane r . (2i+6j+3k) = 70.
Find the orthogonal canonical reduction of the quadratic form
x2+y2 + z2 - 2xy - 2xz - 2yz. Also, find its principal axes.
- Consider the linear operator T : C3 → C3, defined by
T (z1, z2, z3) = (z1 − iz2, iz1 + 2z2 + iz3, −iz2 + z3) .
- Compute T ∗ and check whether T is self-adjoint.
ii) Check whether T is unitary