Dot Product and Cross Product MCQs

Dot Product and Cross Product MCQs – Class 12 Maths

Dot Product and Cross Product MCQs

Class: CBSE Class 12
Subject: Mathematics
Section: Vector Algebra
Topic: Dot Product & Cross Product MCQs
Exam Focus: CBSE Board Examinations

Instructions: These Multiple Choice Questions (MCQs) are strictly based on the NCERT syllabus, making them ideal for CBSE Class 12 Board Examination preparation. Each question includes detailed explanation for concept clarity.

Q1. Dot product result is:

a) Scalar
b) Vector
c) Matrix
d) Tensor

Answer: a)

Dot product produces a scalar quantity.

Q2. a·b = |a||b| cosθ

a) Dot product formula
b) Cross product
c) STP
d) None

Answer: a)

Q3. If a·b = 0, vectors are:

a) Perpendicular
b) Parallel
c) Equal
d) Opposite

Answer: a)

Q4. Cross product result is:

a) Vector
b) Scalar
c) Number
d) Angle

Answer: a)

Q5. |a×b| equals:

a) |a||b| sinθ
b) cosθ
c) tanθ
d) 0

Answer: a)

Q6. Area of parallelogram:

a) |a×b|
b) a·b
c) |a+b|
d) |a−b|

Answer: a)

Q7. Parallel vectors cross product:

a) 0
b) 1
c) a·b
d) ∞

Answer: a)

Q8. Unit vector perpendicular to a,b:

a) (a×b)/|a×b|
b) a·b
c) a+b
d) None

Answer: a)

Q9. Angle using dot product:

a) cos⁻¹(a·b/|a||b|)
b) sin⁻¹
c) tan⁻¹
d) None

Answer: a)

Q10. a·a =

a) |a|²
b) 0
c) a
d) 1

Answer: a)

Q11. Scalar triple product gives:

a) Volume
b) Area
c) Length
d) Angle

Answer: a)

Q12. Coplanar vectors STP:

a) 0
b) 1
c) a·b
d) ∞

Answer: a)

Q13. |a×b| maximum when θ:

a) 90°
b) 0°
c) 180°
d) 45°

Answer: a)

Q14. |a·b| maximum when θ:

a) 0°
b) 90°
c) 180°
d) 45°

Answer: a)

Q15. Perpendicular vectors cross product magnitude:

a) |a||b|
b) 0
c) 1
d) ∞

Answer: a)

Q16. Direction of a×b by:

a) Right hand rule
b) Left hand rule
c) Dot rule
d) None

Answer: a)

Q17. a×a =

a) 0
b) a
c) 1
d) ∞

Answer: a)

Q18. Orthogonal vectors dot product:

a) 0
b) 1
c) −1
d) ∞

Answer: a)

Q19. Cross product useful for:

a) Area & direction
b) Length
c) Angle only
d) None

Answer: a)

Q20. Dot product useful for:

a) Angle
b) Area
c) Volume
d) Direction

Answer: a)

Used to find angle & projection.

Dot Product and Cross Product MCQs

Dot Product and Cross Product MCQs

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