The scalar product of two vectors is negative when:
Correct answer: B. They are anti-parallel vectors
- A. They are parallel vectors
- B. They are anti-parallel vectors
- C. They are perpendicular vectors
- D. They are parallel with some magnitude
Explanation
(a) They are parallel vectors: When two vectors are parallel, the dot product (scalar product) of the vectors will be positive or zero. The dot product will only be negative if the vectors are anti-parallel, not parallel. (b) They are anti-parallel vectors: When two vectors are anti-parallel, meaning they have opposite directions, the dot product of the vectors will be negative. This is the correct option given. (c) They are perpendicular vectors: When two vectors are perpendicular to each other, the dot product of the vectors will be zero. It is not negative. (d) They are parallel with some magnitude: If two vectors have the same direction but different magnitudes, the dot product will be positive or zero. It will not be negative. So, in summary, the correct option is (b) - the scalar product of two vectors is negative when they are anti-parallel, meaning they have opposite directions.
Report an error
The more specific you are, the faster it gets fixed. A source beats an opinion.
Prefer email? [email protected]
About Vectors and Equilibrium
Vectors have magnitude and direction, unlike scalars, and are combined by head-to-tail or parallelogram methods. Work covers rectangular components, equilibrium when the resultant force is zero, the scalar product for work and projections, and the vector product for torque and cross-product direction using the right-hand rule.
Practise Vectors and Equilibrium
431 free Vectors and Equilibrium MCQs from Physics, each with the correct answer and an explanation. Unlimited attempts, no account needed.
Discussion
Stuck on an option, or know a faster way to get there? Ask or explain it here.
No comments yet. Be the first to explain this one.
Exams that ask Physics questions like this
Physics is on 16 papers prepared for on TestUstad, and all of them draw the same bank, so this question is worth knowing for every one of them.
More Vectors and Equilibrium questions
For a vector V:
If two non-zero vectors a and b are parallel to each other, then:
Dot product of two non-zero vectors is zero ( a . b = 0) when angle between them is be:
The cross product of two parallel vectors A and B (i.e. A x B) is equal to:
The magnitude of.....
If the dot product of two non-zero vectors A and B is zero, their cross product will be of magnitude: