The Question is from neet-physics motion-in-a-plane , and it was created by the author Mr. ANIL KUMAR.G

Question

The resultant of two vector of equal magnitude is twice of magnitude of either of the vectors the angle between them is

Mr. ANIL KUMAR.G · Accepted Answer

## CORE INFORMATION
✓ **Answer**: C
## CONCEPT FRAMEWORK
**Primary Concept**: Vector Addition
**Related Topics**: Resultant Vector, Dot Product, Angle between vectors.
**Prerequisites**: Understanding of vector addition and the relationship between resultant magnitude and angle between vectors.
## SOLUTION PATHWAY
**Given Information**:
    * Two vectors with equal magnitude, let's say A.
    * Resultant magnitude is twice of the magnitude of each vector, i.e., 2A.
**Method & Steps**:
    1. Let the two vectors be $\vec{A}$ and $\vec{B}$, with $|\vec{A}| = |\vec{B}| = A$. Let the angle between them be $	heta$.
        Reasoning: We are given that the magnitude of the vectors are same and we are to calculate the angle between them.
       Formula/Rule: The magnitude of the resultant vector $\vec{R}$ of two vectors $\vec{A}$ and $\vec{B}$ is given by: $|\vec{R}| = \sqrt{|\vec{A}|^2 + |\vec{B}|^2 + 2|\vec{A}||\vec{B}|cos(	heta)}$
    2.  We are given that the magnitude of the resultant vector is 2A, i.e., $|\vec{R}|=2A$. Substitute the given values in the formula:
        Working: $2A = \sqrt{A^2 + A^2 + 2(A)(A)cos(	heta)}$
        Key Point: We need to solve for $	heta$.
    3. Squaring both sides of the equation:
        Working: $4A^2 = 2A^2 + 2A^2cos(	heta)$ or $2A^2 = 2A^2cos(	heta)$, which simplifies to $cos(	heta) = 1$
    4.  Solving for $	heta$:
         Result:  $	heta = cos^{-1}(1) = 0^0$
         Verification: This result makes sense, because when the angle is zero the vectors are in the same direction and their magnitudes simply add up.
## OPTION ANALYSIS
[A] :x: $60^0$ would not yield a resultant of twice the magnitude of the individual vectors.
[B] :x: $120^0$ would result in a resultant equal to the individual vectors, not twice.
[C] ✓: $0^0$ results in the vectors being in the same direction, and their magnitudes are additive, hence, the resultant is twice the individual magnitudes.
[D] :x:  $180^0$ would result in a resultant of zero as the vectors would cancel each other.
## LEARNING AIDS
**Common Mistakes**:
    1.  Forgetting the cosine term in the resultant vector magnitude formula: This can lead to incorrect calculations.
    2.  Incorrectly solving the trigonometric equation: Ensure you are using the correct inverse trigonometric function.
**Quick Tips**:
    1. Remember that when vectors point in the same direction, their magnitudes add directly.
    2. When vectors point in the opposite direction, their magnitudes subtract directly.

Mr. ANIL KUMAR.G · Answer

${60^0}$

Mr. ANIL KUMAR.G · Answer

${120^0}$

Mr. ANIL KUMAR.G · Answer

The correct Option is "${0^0}$"

Mr. ANIL KUMAR.G · Answer

${180^0}$

NEET Physics Motion In A Plane MCQs

Select Topic

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

NEET Subjects

Our Bots

Company