Unit 14 Class 11 Math Notes – Vectors in Space (Punjab Board New Book)
Unit 14 (Chapter 14) Class 11 Math Notes – Vectors in Space: step-by-step solutions of Exercise 14.1, Exercise 14.2, Exercise 14.3 and Exercise 14.4 for the Punjab Board new book (1st Year). Tap an exercise below to open its PDF solution, then view it online or download it.
This unit is part of our Class 11 maths notes for the Punjab Board new book, where you can open the solutions of the other units.
Exercise Wise Solutions of Unit 14 Class 11 Math
What Each Exercise of Unit 14 Covers
Exercise 14.1 – Vectors and Their Operations
Exercise 14.1 has 12 questions on vector operations, magnitude, unit vectors, direction cosines, parallel vectors and displacement.
Exercise 14.2 – Dot Product
Exercise 14.2 has 16 questions on the dot product: angle between vectors, projections, perpendicularity, right triangles, proofs and work done.
Exercise 14.3 – Cross Product
Exercise 14.3 has 16 questions on the cross product: unit normals, areas, parallel and perpendicular vectors, proofs and the moment of a force.
Exercise 14.4 – Scalar Triple Product
Exercise 14.4 has 15 questions on the scalar triple product: volumes, coplanarity, torque, and sales and profit problems.
Key Formulas of Unit 14 Class 11 Math
- \(|\mathbf v|=\sqrt{a^2+b^2+c^2}\) for \(\mathbf v=a\mathbf i+b\mathbf j+c\mathbf k\).
- \(\mathbf a\cdot\mathbf b=|\mathbf a||\mathbf b|\cos\theta\)
- \(|\mathbf a\times\mathbf b|=|\mathbf a||\mathbf b|\sin\theta\)
- Area of triangle \(PQR=\tfrac12|\overrightarrow{PQ}\times\overrightarrow{PR}|\).
- Volume of a parallelepiped \(=|[\mathbf u\ \mathbf v\ \mathbf w]|\); the vectors are coplanar if it is 0.
Related Class 11 Math Notes
Continue with Unit 13 Class 11 Math Notes, or go back to the Class 11 maths notes hub for all 14 units.
FAQs About Unit 14 Class 11 Math
How many exercises are there in Unit 14?
Unit 14 has four exercises: Exercise 14.1, 14.2, 14.3 and 14.4.
Which exercise has the work done, moment and torque problems?
Work done is in Exercise 14.2 (dot product), the moment of a force is in Exercise 14.3 (cross product), and torque is in Exercise 14.4 (scalar triple product).
Are these notes for the new book?
Yes. These solutions are for the new Class 11 mathematics book by PECTAA (2025 edition onwards), used by the nine BISE Punjab boards: Lahore, Gujranwala, Faisalabad, Multan, Rawalpindi, Sargodha, Sahiwal, Bahawalpur and Dera Ghazi Khan.