Explore topic-wise MCQs in Linear Algebra.

This section includes 10 Mcqs, each offering curated multiple-choice questions to sharpen your Linear Algebra knowledge and support exam preparation. Choose a topic below to get started.

1.

Express V in terms of Spherical coordinates where V = x + y2z + z3x.

A. rsin u2061 cos u2061 + r<sup>3</sup>sin u2061 <sup>2</sup> sin u2061 cos u2061 + r<sup>4</sup>sin u2061 cos u2061 <sup>3</sup> cos u2061
B. rsin u2061 cos u2061 + r<sup>2</sup>sin u2061 <sup>3</sup> sin u2061 cos u2061 + r<sup>4</sup>sin u2061 cos u2061 <sup>3</sup> cos u2061
C. rsin u2061 cos u2061 + r<sup>3</sup>sin u2061 <sup>2</sup> sin u2061 cos u2061 + r<sup>4</sup>sin u2061 cos u2061 <sup>2</sup> cos u2061
D. rsin u2061 cos u2061 + r<sup>3</sup>sin u2061 <sup>3</sup> sin u2061 cos u2061 + r<sup>4</sup>sin u2061 cos u2061 <sup>2</sup> cos u2061
Answer» B. rsin u2061 cos u2061 + r<sup>2</sup>sin u2061 <sup>3</sup> sin u2061 cos u2061 + r<sup>4</sup>sin u2061 cos u2061 <sup>3</sup> cos u2061
Discussion
2.

What is the value of ar.ax?

A. sin u2061 cos u2061
B. sin u2061 sin u2061
C. cos u2061 cos u2061
D. cos u2061 sin u2061
Answer» B. sin u2061 sin u2061
Discussion
3.

Find the distance between A(10, 30,60) and B(8, 60, 90).

A. 4
B. 5
C. 6
D. 7
Answer» D. 7
Discussion
4.

Convert U = xyz + y + xz into Cylindrical coordinates.

A. z <sup>3</sup>sin u2061 cos u2061 + sin u2061 + z cos u2061
B. z <sup>2</sup>sin u2061 cos u2061 + sin u2061 + z cos u2061
C. z <sup>3</sup>sin u2061 cos u2061 + 2sin u2061 + z cos u2061
D. z <sup>2</sup>sin u2061 cos u2061 + 2sin u2061 + z cos u2061
Answer» C. z <sup>3</sup>sin u2061 cos u2061 + 2sin u2061 + z cos u2061
Discussion
5.

What is the value of az . ar?

A. 1
B. cos u2061
C. sin u2061
D. 0
Answer» C. sin u2061
Discussion
6.

Find the distance between two points A(5,60.,0) and B(10,90.,0) where the points are given in Cylindrical coordinates.

A. 4.19 units
B. 5.19 units
C. 6.19 units
D. 7.19 units
Answer» D. 7.19 units
Discussion
7.

Convert the vector P to Cartesian coordinates where P = r ar + cos a .

A. ( frac{1}{ sqrt{x^2+y^2+z^2}} [( frac{x}{ sqrt{x^2+y^2+z^2}}- frac{xyz}{ sqrt{x^2+y^2 }})az + ( frac{y}{ sqrt{x^2+y^2+z^2}}+ frac{xyz}{ sqrt{x^2+y^2}})ay+ frac{z}{ sqrt{x^2+y^2+z^2}} ax] )
B. ( frac{1}{ sqrt{x^2+y^2+z^2}} [( frac{x}{ sqrt{x^2+y^2+z^2}}- frac{yz}{ sqrt{x^2+y^2 }})ax + ( frac{y}{ sqrt{x^2+y^2+z^2}}+ frac{xz}{ sqrt{x^2+y^2}})ay+ frac{z}{ sqrt{x^2+y^2+z^2}} az] )
C. ( frac{1}{ sqrt{x^2+y^2+z^2}} [( frac{x}{ sqrt{x^2+y^2+z^2}}- frac{y}{ sqrt{x^2+y^2 }})ax + ( frac{y}{ sqrt{x^2+y^2+z^2}}+ frac{z}{ sqrt{x^2+y^2}})ay+ frac{z}{ sqrt{x^2+y^2+z^2}} az] )
D. ( frac{1}{ sqrt{x^2+y^2+z^2}} [( frac{x}{ sqrt{x^2+y^2+z^2}}- frac{y}{ sqrt{x^2+y^2 }})ax + ( frac{y}{ sqrt{x^2+y^2+z^2}}+ frac{x}{ sqrt{x^2+y^2}})ay+ frac{z}{ sqrt{x^2+y^2+z^2}} az] )
Answer» C. ( frac{1}{ sqrt{x^2+y^2+z^2}} [( frac{x}{ sqrt{x^2+y^2+z^2}}- frac{y}{ sqrt{x^2+y^2 }})ax + ( frac{y}{ sqrt{x^2+y^2+z^2}}+ frac{z}{ sqrt{x^2+y^2}})ay+ frac{z}{ sqrt{x^2+y^2+z^2}} az] )
Discussion
8.

Let there be a vector X = yz2 ax + zx2 ay + xy2 az. Find X at P(3,6,9) in cylindrical coordinates.

A. 100 a<sub>x</sub> 398 a<sub>y</sub> + 108 a<sub>z</sub>
B. 103 a<sub>x</sub> 401 a<sub>y</sub> + 109 a<sub>z</sub>
C. 105 a<sub>x</sub> 393 a<sub>y</sub> + 105 a<sub>z</sub>
D. 95 a<sub>x</sub> 395 a<sub>y</sub> + 100 a<sub>z</sub>
Answer» B. 103 a<sub>x</sub> 401 a<sub>y</sub> + 109 a<sub>z</sub>
Discussion
9.

Convert the (10, 90, 60) coordinates to Cartesian coordinates which are in Spherical coordinates.

A. (5, 8.66, 10)
B. (5, 8.66, 0)
C. (10, 5, 8.66)
D. (0, 5, 8.66)
Answer» C. (10, 5, 8.66)
Discussion
10.

Convert Cartesian coordinates (2, 6, 9) to Cylindrical and Spherical Coordinates.

A. (6.32, 71.565., 6.32) and (11, 71.565., 35.097)
B. (6.32, 71.565., 9) and (6.32, 71.565., 35.097)
C. (6.32, 71.565., 6.32) and (6.32, 35.097., 71.565)
D. (6.32, 71.565., 9) and (11, 35.097., 71.565)
Answer» E.
Discussion