JEE 2023 — Mathematics PYQ

Q: How do I solve JEE 2023 Mathematics questions?

Practice JEE 2023 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 JEE Mathematics questions?

JEE 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 JEE previous year papers available for free?

Yes. Mathem Solvex provides free access to JEE 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

JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

If four distinct points with position vectors $\vec{a}, \vec{b}, \vec{c}$ and $\vec{d}$ are coplanar, then $[\vec{a}\vec{b}\vec{c}]$ is equal to:

Choose the correct answer:

Explanation

Solution

Agar char points $A(\vec{a}), B(\vec{b}), C(\vec{c}), D(\vec{d})$ coplanar hain, toh vectors $\vec{AB}, \vec{AC}, \vec{AD}$ bhi coplanar honge. Unka Scalar Triple Product zero hoga:

[\vec{b}-\vec{a} \quad \vec{c}-\vec{a} \quad \vec{d}-\vec{a}] = 0

Ise expand karne par:

(\vec{b}-\vec{a}) \cdot [(\vec{c}-\vec{a}) \times (\vec{d}-\vec{a})] = 0

(\vec{b}-\vec{a}) \cdot [\vec{c} \times \vec{d} - \vec{c} \times \vec{a} - \vec{a} \times \vec{d} + \vec{a} \times \vec{a}] = 0

Kyunki $\vec{a} \times \vec{a} = 0$ , bache hue terms ka dot product lene par:

[\vec{b}\vec{c}\vec{d}] - [\vec{b}\vec{c}\vec{a}] - [\vec{b}\vec{a}\vec{d}] - [\vec{a}\vec{c}\vec{d}] + [\vec{a}\vec{c}\vec{a}] + [\vec{a}\vec{a}\vec{d}] = 0

[\vec{b}\vec{c}\vec{d}] - [\vec{b}\vec{c}\vec{a}] + [\vec{b}\vec{d}\vec{a}] + [\vec{d}\vec{c}\vec{a}] = 0

[\vec{a}\vec{b}\vec{c}] = [\vec{b}\vec{c}\vec{d}] + [\vec{d}\vec{c}\vec{a}] + [\vec{b}\vec{d}\vec{a}]

Agar hum cyclic order aur signs ko adjust karein (Property: $[\vec{b}\vec{d}\vec{a}] = [\vec{d}\vec{b}\vec{a}]$ in some options), toh option (4) match karta hai.

Sahi Option: (4)

Choose the correct answer:

Explore More