Published by:
CGP EDU Academic Team
Published on: September 12, 2026
The diagonals of a parallelogram are 2\hat{i} and 2\hat{j} What is the area of the parallelogram
Text Solution
Verified by ExpertsThe correct answer is:
C
For a parallelogram, if diagonals are \vec{d}_1 and \vec{d}_2 , then
\(\mathrm{Area} = \frac{1}{2} \left| \vec{d}_1 \times \vec{d}_2 \right|\)
Given:
\vec{d}_1 = 2\hat{i}, \vec{d}_2 = 2\hat{j}
\(\vec{d}_1 \times \vec{d}_2 = (2\hat{i}) \times (2\hat{j}) = 4(\hat{i} \times \hat{j}) = 4\hat{k}\)
\(\left|\vec{d}_1 \times \vec{d}_2\right| = 4\)
Therefore,
\(\textbf{Area} = \frac{1}{2} \times 4 = 2\)
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
If a vector 2\hat{i} + 3\hat{j} + 8\hat{k} is perpendicular to the vector \(4\hat{i} - 4\hat{j} + \…
If two vectors 2\hat{i} + 3\hat{j} - \hat{k} and \(-4\hat{i} - 6\hat{j} - \lambda \hat{k}\) are par…
A body, acted upon by a force of 50 N is displaced through a distance 10 meter in a direction makin…
A particle moves from position 3\hat{i} + 2\hat{j} - 6\hat{k} to 14\hat{i} + 13\hat{j} + 9\hat{k} d…
If for two vector \vec{A} and \vec{B} , sum \(\left(\vec{A} + \vec{B}\right)\) is perpendicular to …
The angle between the vectors \vec{A} and \vec{B} is \(\theta.\) The value of the triple product \(…