Two vectors of magnitude 3 & 4 have a resultant of 5. The angle between vectors is :
Correct answer: A. 90°
- A. 90°
- B. 45°
- C. 180°
- D. 270°
Explanation
The problem involves finding the angle between two vectors with magnitudes 3 and 4, resulting in a magnitude of 5 for their resultant vector. Applying the law of cosines to the vectors: |R|2 = |P|2 + |Q|2 + 2|P||Q|cos∅, we substitute in the given magnitudes: 52 = 32 + 42 + 2(3)(4)cos∅. Simplifying gives 25 = 9 + 16 + 24cos∅. Solving for cos∅, we find cos∅ = 0, which means ∅ = 90°. Thus, the vectors are perpendicular. Other options such as 45°, 180°, and 270° do not satisfy the geometric and trigonometric constraints of the problem.
Report an error
The more specific you are, the faster it gets fixed. A source beats an opinion.
Prefer email? [email protected]
About Addition of Vectors
Vector addition combines directed quantities using the head-to-tail, parallelogram and component methods. Work includes finding the resultant magnitude and direction for two or more vectors, resolving vectors into perpendicular components, and distinguishing vector addition from scalar addition, where direction has no role.
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 Addition of Vectors questions
Two vectors each of magnitude F make angle 0° and 270° with x-axis. Their resultant is:
Resultant of two forces 30N and 40N acting perpendicular to each other is
Find the angle between two forces of equal magnitude when the magnitude of their resultant is also equal to the magnitude of either of these forces:
The vector addition follows:
What angle would it require to have for vectors of the same length to achieve a resultant of twice the amount in either.
If two forces P and Q are such that |P + Q| = |P - Q|, then the angle between P and Q is: