The Question is from neet-physics motion-in-a-plane addition-subtraction-and-resolution-of-vectors, and it was created by the author ABDUL JILANI BASHA

Question

The vector that must be added to the vector $\widehat i - 3\widehat j + 2\widehat k\,and\,3\widehat i + 6\widehat j - 7\widehat k$ so that the resultant  vector is a unit vector along the y-axis is

ABDUL JILANI BASHA · Accepted Answer

## CORE INFORMATION
✓ **Answer**: B
## CONCEPT FRAMEWORK
	**Primary Concept**: Vector Addition
	**Related Topics**: Unit Vectors, Resultant Vectors
	**Prerequisites**: Understanding of vector components and unit vectors.
## SOLUTION PATHWAY
**Given Information**:
	* Vector 1: $\vec{A} = \widehat i - 3\widehat j + 2\widehat k$
	* Vector 2: $\vec{B} = 3\widehat i + 6\widehat j - 7\widehat k$
	* Resultant Vector: $\vec{R} = 0\widehat i + 1\widehat j + 0\widehat k = \widehat j$ (unit vector along y-axis)
	* Let the unknown vector be $\vec{C}$
**Method & Steps**:
	1. Calculate the sum of the given vectors $\vec{A}$ and $\vec{B}$:
		Reasoning: Add corresponding components of the vectors.
		Formula/Rule: $\vec{A} + \vec{B} = (A_x + B_x)\widehat i + (A_y + B_y)\widehat j + (A_z + B_z)\widehat k$
	2.  $\vec{A} + \vec{B} = (1+3)\widehat i + (-3+6)\widehat j + (2-7)\widehat k = 4\widehat i + 3\widehat j - 5\widehat k$
		Working: Vector addition is component-wise.
		Key Point: Combine like terms correctly.
	3. Find the vector $\vec{C}$ by subtracting the sum of $\vec{A}$ and $\vec{B}$ from the resultant vector $\vec{R}$:
		Reasoning: $\vec{A} + \vec{B} + \vec{C} = \vec{R}$, so $\vec{C} = \vec{R} - (\vec{A} + \vec{B})$
	4. $\vec{C} = \widehat j - (4\widehat i + 3\widehat j - 5\widehat k) = -4\widehat i + (1-3)\widehat j + 5\widehat k = -4\widehat i - 2\widehat j + 5\widehat k$
		Result: The required vector is $\vec{C} = -4\widehat i - 2\widehat j + 5\widehat k$
		Verification: Adding $\vec{C}$ to $\vec{A} + \vec{B}$ gives $\widehat j$.
 ## OPTION ANALYSIS
[A] :x: Incorrect. Adding this vector to the sum of the given vectors does not result in $\widehat j$.
[B] ✓: Correct. Adding this vector to the sum of the given vectors results in $\widehat j$.
[C] :x: Incorrect. Adding this vector to the sum of the given vectors does not result in $\widehat j$.
[D] :x: Incorrect. Adding a null vector to the sum of the given vectors does not result in $\widehat j$.
 ## LEARNING AIDS
	**Common Mistakes**:
		1. [Error 1]: Incorrectly adding or subtracting vector components.
			[How to avoid]: Ensure each component is handled separately and with correct signs.
		2. [Error 2]: Confusing vector addition with scalar addition.
			[How to avoid]: Always add or subtract corresponding components of the vectors.
	**Quick Tips**:
		1. [Helpful shortcut]:  Write out each component separately before performing addition/subtraction.
		2. [Memory aid]: Remember that the unit vector along the y-axis is $\widehat j$ or $0\widehat i + 1\widehat j + 0\widehat k$.

ABDUL JILANI BASHA · Answer

$4\widehat i + 2\widehat j + 5\widehat k$

ABDUL JILANI BASHA · Answer

The correct Option is "$ - 4\widehat i - 2\widehat j + 5\widehat k$"

ABDUL JILANI BASHA · Answer

$3\widehat i + 4\widehat j + 5\widehat k$

ABDUL JILANI BASHA · Answer

Null Vector

NEET Physics Motion In A Plane Addition,Subtraction And Resolution Of Vectors MCQs

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