The Question is from neet-chemistry , and it was created by the author Mr. S M HUSSAIN

Question

The area of the parallelogram represented by the vectors. ${\rm{\vec A}} = 4\hat i + 3\hat j\,\,and\,{\rm{\vec B}} = 2\hat i + 4\hat j$ is

Mr. S M HUSSAIN · Accepted Answer

## CORE INFORMATION
✓ **Answer**: C
## CONCEPT FRAMEWORK
	**Primary Concept**: Area of a parallelogram formed by two vectors.
	**Related Topics**: Vector cross product, determinants.
	**Prerequisites**: Understanding of vector representation, calculation of cross product in 2D.
## SOLUTION PATHWAY
**Given Information**:
	Vector A:  $\vec{A} = 4\hat{i} + 3\hat{j}$
	Vector B:  $\vec{B} = 2\hat{i} + 4\hat{j}$
	We want the area of the parallelogram.
**Method & Steps**:
	1. The area of the parallelogram formed by two vectors is the magnitude of the cross product of the two vectors.
		Reasoning: The cross product gives a vector perpendicular to the plane formed by the two vectors, and its magnitude is equal to the area of the parallelogram.
		Formula/Rule: Area = $|\vec{A} 	imes \vec{B}|$
	2. Calculate the cross product of the two vectors. Since these are 2D vectors, we can calculate the magnitude of the cross product using the determinant method:
		Working: $\vec{A} 	imes \vec{B} = \begin{vmatrix}  \hat{i} & \hat{j} & \hat{k} \ 4 & 3 & 0 \ 2 & 4 & 0 \end{vmatrix} = (4*4 - 3*2)\hat{k} = (16-6)\hat{k} = 10\hat{k}$ 
		Key Point: Since the vectors are in the xy plane, the cross product will be in the z direction.
	3. Find the magnitude of the resulting vector.
		Result: $|10\hat{k}| = 10$
		Verification: The magnitude is the area, which is 10 units.
 ## OPTION ANALYSIS
[A] :x: Incorrect. This is likely the result of adding the components or a miscalculation.
[B] :x: Incorrect.  This is not derived from the correct method.
[C] ✓: Correct.  The area is the magnitude of the cross product, which is 10.
[D] :x: Incorrect.  This is not derived from the correct method.
 ## LEARNING AIDS
	**Common Mistakes**:
		1.[Error 1]: Forgetting to take the magnitude of the cross product.  [How to avoid]: Remember that the area is a scalar quantity and the cross product is a vector. Take the magnitude.
		2.[Error 2]: Incorrectly calculating the determinant. [How to avoid]: Practice determinant calculations for 2x2 and 3x3 matrices.
	**Quick Tips**:
		1.[Helpful shortcut]: In 2D, the magnitude of the cross product is just the absolute value of $A_xB_y - A_yB_x$.
		2.[Memory aid]: Remember the cross product gives you a vector perpendicular to the plane of the vectors, and its magnitude is the area.

Mr. S M HUSSAIN · Answer

14 units

Mr. S M HUSSAIN · Answer

7.5 units

Mr. S M HUSSAIN · Answer

The correct Option is "10 units"

Mr. S M HUSSAIN · Answer

5 units

NEET Chemistry MCQs

Select Chapter

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