NIMCET 2013 — Mathematics PYQ

Q: How do I solve NIMCET 2013 Mathematics questions?

Practice NIMCET 2013 Mathematics previous year questions with step-by-step solutions on Mathem Solvex. Each question includes a detailed explanation and video solution to help you master the concept quickly.

Q: What is the difficulty level of NIMCET Mathematics questions?

NIMCET Mathematics questions range from moderate to advanced difficulty. Consistent practice with official previous year papers and topic-wise drills on Mathem Solvex is the most effective preparation strategy.

Q: Are NIMCET previous year papers available for free?

Yes. Mathem Solvex provides free access to NIMCET previous year question papers and topic-wise PDFs. You can download them or attempt them as timed live mock tests directly on the platform.

Question

NIMCET 2013 — Mathematics PYQ

NIMCET | Mathematics | 2013

The area of the parallelogram whose diagonals are $\vec{a} = 3\hat{i} + \hat{j} - 2\hat{k}$ and $\vec{b} = \hat{i} - 3\hat{j} + 4\hat{k}$ is:

Choose the correct answer:

Explanation

Solution

1. Formula for Area using Diagonals:

When the diagonals of a parallelogram are given as vectors $\vec{d_1}$ and $\vec{d_2}$ , the area is:

\text{Area} = \frac{1}{2} |\vec{d_1} \times \vec{d_2}|

2. Calculate the Cross Product ( $\vec{a} \times \vec{b}$ ):

\vec{a} \times \vec{b} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 3 & 1 & -2 \\ 1 & -3 & 4 \end{vmatrix}

\vec{a} \times \vec{b} = \hat{i}(4 - 6) - \hat{j}(12 - (-2)) + \hat{k}(-9 - 1)

\vec{a} \times \vec{b} = -2\hat{i} - 14\hat{j} - 10\hat{k}

3. Calculate the Magnitude of the Cross Product:

|\vec{a} \times \vec{b}| = \sqrt{(-2)^2 + (-14)^2 + (-10)^2}

|\vec{a} \times \vec{b}| = \sqrt{4 + 196 + 100}

|\vec{a} \times \vec{b}| = \sqrt{300}

|\vec{a} \times \vec{b}| = 10\sqrt{3}

4. Calculate the Final Area:

\text{Area} = \frac{1}{2} \times 10\sqrt{3}

\text{Area} = 5\sqrt{3}

Choose the correct answer:

Explore More