NEET Physics: Resolution of a Vector Practice Questions
9 free multiple-choice questions on Resolution of a Vector (Kinematics) for NEET Physics, each with the correct answer and a step-by-step explanation. Attempt a question, then reveal the solution to check your reasoning.
Practice thousands more NEET questions in the app →Q1. What is the direction of a vector P⃗ if its components are Pₓ = 3 and P_y = -4?
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Correct answer: B — 180° - tan⁻¹(4/3)
The angle θ is found using tan θ= P_y / Pₓ. tan θ= -4/3. Since Pₓ is positive and P_y is negative, the angle is in the fourth quadrant. θ= tan⁻¹(-4/3).
Q2. If a vector has components Aₓ = 3 units and A_y = 4 units, what is the magnitude of the vector?
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Correct answer: B — 5
The magnitude R is calculated using the Pythagorean theorem: R = √(Aₓ² + A_y²) = √(3² + 4²) = √(9 + 16) = √25 = 5
Q3. If the x-component of a vector is 4 units and the y-component is 3 units, what is the magnitude of the vector?
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Correct answer: D — 1 unit
The magnitude of a vector (R) given its components (Aₓ and A_y) is found using the Pythagorean theorem: R = √(Aₓ² + A_y²). R = √(4² + 3²) = √(16 + 9) = √25 = 5 units.
Q4. A displacement vector d⃗ has a magnitude of 10 units and makes an angle of 60° with the positive x-axis. What is the component of d⃗ along the y-axis?
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Correct answer: D — 8.66
The y-component is given by d_y = d sin(θ). Here, d_y = 10 sin(60°) = 10 (√3/2) ≈ 8.66 units.
Q5. A force vector F⃗ has a magnitude of 10 N and acts at an angle of 30° with the positive x-axis. What is the component of the force acting along the x-axis?
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Correct answer: C — 5√3 N
The component of a vector F⃗ along the x-axis is given by Fₓ = F cos θ. Here, Fₓ = 10 cos(30°) = 10 × √3/2 = 5√3 N.
Q6. A vector D⃗ has a magnitude of 5. If D⃗ is resolved into components D⃗ₓ and D⃗_y, which relationship must hold true?
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Correct answer: D — √(Dₓ² + D_y²) = 5
The magnitude of the vector is the hypotenuse formed by its components. By the Pythagorean theorem, √(Dₓ² + D_y²) must equal the magnitude of the vector, which is 5.
Q7. If two vectors P⃗ and Q⃗ are perpendicular to each other, what is the magnitude of their resultant vector R⃗ = P⃗ + Q⃗?
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Correct answer: B — √(|P⃗|² + |Q⃗|²)
If two vectors are perpendicular, the magnitude of their resultant is found using the Pythagorean theorem: |R⃗| = √(|P⃗|² + |Q⃗|²).
Q8. A vector C⃗ is resolved into its components along the x and y axes. If Cₓ = 6 and C_y = 8, what is the magnitude of vector C⃗?
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Correct answer: D — 10
The magnitude of the vector is found using the Pythagorean theorem: |C⃗| = √(Cₓ² + C_y²). Magnitude = √(6² + 8²) = √(36 + 64) = √100 = 10.
Q9. The direction cosines of a vector A⃗ are the cosines of the angles it makes with the x, y, and z axes. If the vector lies along the positive x-axis, what is the value of its direction cosine with respect to the x-axis?
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Correct answer: B — 1
Direction cosines are (cos α, cos β, cos γ), where α, β, γ are the angles with the x, y, and z axes, respectively. If the vector lies exactly along the positive x-axis, the angle with the x-axis is 0°, so the cosine is cos(0°) = 1.
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