# Electromagnetic Theory Questions and Answers – Dot and Cross Product

This set of Electromagnetic Theory Multiple Choice Questions & Answers (MCQs) focuses on “Dot and Cross Product”.

1. When two vectors are perpendicular, their
a) Dot product is zero
b) Cross product is zero
c) Both are zero
d) Both are not necessarily zero

Explanation: Dot product of two perpendicular vectors is given by A.B = |a||b|cos 90, which is zero. Thus, dot product is zero and vectors are perpendicular.

2. The cross product of the vectors 3i + 4j – 5k and –i + j – 2k is,
a) 3i – 11j + 7k
b) -3i + 11j + 7k
c) -3i – 11j – 7k
d) -3i + 11j – 7k

Explanation: Cross product of two vectors is, A X B = (a2*b3 – b2*a3)i – (a1*b3 – b1*a3)j + (a1*b2 – b1*a2)k. Using the formula, the answer can be calculated.

3. Which of the following are not vector functions in Electromagnetics?
b) Divergence
c) Curl
d) There is no non- vector functions in Electromagnetics

Explanation: Since all the coordinates in electromagnetic are space coordinates, direction and magnitude both are important. Thus all functions are vector only.

4. The work done of vectors force F and distance d, separated by angle θ can be calculated using,
a) Cross product
b) Dot product
d) Cannot be calculated

Explanation: Force is a vector quantity, whereas distance is scalar. Work is defined as the product of force and distance, which is given by dot product.

5. Find whether the vectors are parallel, (-2,1,-1) and (0,3,1)
a) Parallel
b) Collinearly parallel
c) Not parallel
d) Data insufficient

Explanation: Two vectors are parallel when their cross product is zero. Since their cross product is 4i + 2j – 6k (non-zero), the vectors are not parallel.
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6. Lorentz force is based on,
a) Dot product
b) Cross product
c) Both dot and cross product
d) Independent of both

Explanation: Lorentz force is given by, F = q (v x B).Thus cross product is the answer.

7. Electromagnetic forces are defined by
a) Fleming’s right hand rule
b) Fleming’s left hand rule
d) Ampere law

Explanation: The three left hand fingers denote electric field, magnetic field and wave propagation in free space, analogous to force, magnetic field and current respectively in any conductor.

8. The dot product of two vectors is a scalar. The cross product of two vectors is a vector. State True/False.
a) True
b) False

Explanation: Dot product is an algebraic operation that takes two equal length sequences and returns a scalar. Cross product is a binary operation that calculates area of two vectors, thus vector quantity.

9. Which of the Pythagorean Theorem is valid in Electromagnetics?
a) |dot product| + |dot product| = 1
b) |cross product| – |cross product| = 1
c) |dot product|2 + |cross product|2 = 1
d) |dot product| + |cross product| = 0

Explanation: Option |dot product|2 + |cross product|2 = 1 gives |cos|2 + |sin|2 = 1, which is the right answer.

10. Which of the following is not true?
a) A . (B . C) = scalar value
b) A . (B x C) = scalar value
c) A x (B . C) = scalar value
d) A x (B x C) = vector value

Explanation: Cross product of dot product of two vectors is a vector value.

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