Vidaara.orgClass 12 · Mathematics
CodeVID-M12-10-CT
Vector Algebra — Full Chapter Test
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- This is a full-length test covering the whole chapter — every topic is included.
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
$|3\hat i+4\hat j|=$
- A.$5$
- B.$7$
- C.$12$
- D.$25$
2.
The dot product of two vectors is a:
- A.vector
- B.scalar
- C.matrix
- D.unit vector
3.
The cross product of two vectors is a:
- A.scalar
- B.vector
- C.number
- D.angle
4.
The unit vector along $2\hat i+3\hat j+6\hat k$ is $\tfrac1k(2\hat i+3\hat j+6\hat k)$ with $k=$
- A.$5$
- B.$7$
- C.$11$
- D.$49$
5.
$\vec a\perp\vec b$ if and only if $\vec a\cdot\vec b=$
- A.$1$
- B.$0$
- C.$|\vec a||\vec b|$
- D.$-1$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Find $|\hat i-2\hat j+2\hat k|$.
7.
Find $(\hat i+\hat j+\hat k)\cdot(\hat i-\hat j+\hat k)$.
8.
Find $(\hat i+\hat j)\times(\hat j+\hat k)$.
9.
Find the unit vector along $3\hat i+4\hat k$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Find the unit vector along $2\hat i+3\hat j+6\hat k$.
11.
Find the angle between $\hat i+\hat j$ and $\hat i$.
12.
Find $\vec a\times\vec b$ for $\vec a=2\hat i+\hat j,\ \vec b=\hat i+2\hat j$.
13.
Find the midpoint of $A(2,0,4)$ and $B(0,2,0)$ as a position vector.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Find a unit vector in the direction of the sum of $\hat i+2\hat j-\hat k$ and $2\hat i+\hat j+\hat k$.
15.
If $|\vec a|=3,\ |\vec b|=4$ and $\vec a\cdot\vec b=6$, find the angle between $\vec a$ and $\vec b$.
Answer Key
Section A — Multiple Choice Questions
- (A) $5$
- (B) scalar
- (B) vector
- (B) $7$
- (B) $0$
Section B — Short Answer (2 marks)
- $3$.
- $1$.
- $\hat i-\hat j+\hat k$.
- $\tfrac15(3\hat i+4\hat k)$.
Section C — Short Answer (3 marks)
- $\tfrac17(2\hat i+3\hat j+6\hat k)$.
- $45^\circ$.
- $3\hat k$.
- $\hat i+\hat j+2\hat k$.
Section D — Long Answer (5 marks)
- $\tfrac{1}{\sqrt2}(\hat i+\hat j)$.
- $60^\circ$.
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