Chapter Exam

Chapter 10: Vector Algebra — Online MCQ Test

Q: A vector is a mathematical quantity that possesses which of the following characteristics?

Answer: C. Both magnitude and direction — By definition, a vector has both magnitude (length) and a definite direction in space.

Q: Find the magnitude of the vector vec{a} = 3î + 4ĵ.

Answer: A. 5 — Magnitude |vec{a}| = √(3² + 4²) = √(9 + 16) = √25 = 5.

Q: Calculate vec{a} · vec{b} for vec{a} = 2î + 3ĵ and vec{b} = 4î + 5ĵ.

Answer: C. 23 — vec{a} · vec{b} = (2)(4) + (3)(5) = 8 + 15 = 23.

Q: Three points A, B, and C are collinear if which condition is satisfied?

Answer: B. vec{AB} × vec{BC} = 0 — Three points are collinear if the vectors formed by them are parallel, which means their cross product is zero.

Q: The vectors vec{a} = xî + ĵ + k̂, vec{b} = î + yĵ + k̂, and vec{c} = î + ĵ + zk̂ are mutually perpendicular. Which statement is correct?

Answer: B. x + y + z = -2 — From vec{a}·vec{b}=0, vec{b}·vec{c}=0, vec{c}·vec{a}=0, we get x+y = -1, y+z = -1, z+x = -1. Solving: x+y+z = -2.

MATHS · Grade 12 · CBSE(NCERT)

Practice Chapter 10: Vector Algebra with a free chapter-wise online MCQ test for CBSE(NCERT) Grade 12 MATHS. This chapter covers: Vector Definition: A vector is a mathematical quantity that possesses both a magnitude (length) and a definite direction in space.Direction Cosines: The direction cosines (l, m, n).... AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter 10: Vector Algebra — Important Questions & Answers (FAQ)

Frequently asked questions from CBSE(NCERT) Grade 12 MATHS — Chapter 10: Vector Algebra, with answers and explanations. These are sample questions; the exam has its own separate question set.

A vector is a mathematical quantity that possesses which of the following characteristics?

A. Only magnitude
B. Only direction
C. Both magnitude and direction ✓
D. Neither magnitude nor direction

Answer: C. Both magnitude and direction
By definition, a vector has both magnitude (length) and a definite direction in space.

Find the magnitude of the vector vec{a} = 3î + 4ĵ.

A. 5 ✓
B. 7
C. 12
D. 25

Answer: A. 5
Magnitude |vec{a}| = √(3² + 4²) = √(9 + 16) = √25 = 5.

Calculate vec{a} · vec{b} for vec{a} = 2î + 3ĵ and vec{b} = 4î + 5ĵ.

A. 8
B. 15
C. 23 ✓
D. 35

Answer: C. 23
vec{a} · vec{b} = (2)(4) + (3)(5) = 8 + 15 = 23.

Three points A, B, and C are collinear if which condition is satisfied?

A. vec{AB} · vec{BC} = 0
B. vec{AB} × vec{BC} = 0 ✓
C. |vec{AB}| = |vec{BC}|
D. vec{AB} + vec{BC} = vec{AC}

Answer: B. vec{AB} × vec{BC} = 0
Three points are collinear if the vectors formed by them are parallel, which means their cross product is zero.

The vectors vec{a} = xî + ĵ + k̂, vec{b} = î + yĵ + k̂, and vec{c} = î + ĵ + zk̂ are mutually perpendicular. Which statement is correct?

A. x = y = z = -1
B. x + y + z = -2 ✓
C. xyz = 1
D. x = 1, y = 1, z = 1

Answer: B. x + y + z = -2
From vec{a}·vec{b}=0, vec{b}·vec{c}=0, vec{c}·vec{a}=0, we get x+y = -1, y+z = -1, z+x = -1. Solving: x+y+z = -2.

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