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Vidaara.orgClass 12 · Mathematics
CodeVID-M12-10-VEC-01
Vectors: Types & Operations — Assignment
Chapter: Vector Algebra
Topic: Vectors: Types & Basic Operations
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • 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 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.$49$
3.
$\overrightarrow{AB}$ equals:
  • A.$\vec a+\vec b$
  • B.$\vec b-\vec a$
  • C.$\vec a-\vec b$
  • D.$\tfrac{\vec a+\vec b}{2}$
4.
A unit vector has magnitude:
  • A.$0$
  • B.$1$
  • C.any value
  • D.$\sqrt2$
5.
The position vector of $P(x,y,z)$ is:
  • A.$x+y+z$
  • B.$x\hat i+y\hat j+z\hat k$
  • C.$\sqrt{x^2+y^2+z^2}$
  • D.$xyz$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find $|\hat i-2\hat j+2\hat k|$.
7.
Find the unit vector along $3\hat i+4\hat k$.
8.
Find $\overrightarrow{AB}$ for $A(1,2,3),\ B(4,6,3)$.
9.
Are $2\hat i+4\hat j$ and $\hat i+2\hat j$ parallel?
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 midpoint of $A(2,0,4)$ and $B(0,2,0)$ as a position vector.
12.
Find a vector of magnitude $10$ along $3\hat i+4\hat j$.
13.
Find the point dividing $A(1,2,3),\ B(4,5,6)$ in the ratio $2:1$.
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.
Show that the points $A(1,2,3),\ B(2,3,4),\ C(3,4,5)$ are collinear.

Answer Key

Section A — Multiple Choice Questions
  1. (A) $5$
  2. (B) $7$
  3. (B) $\vec b-\vec a$
  4. (B) $1$
  5. (B) $x\hat i+y\hat j+z\hat k$
Section B — Short Answer (2 marks)
  1. $3$.
  2. $\tfrac15(3\hat i+4\hat k)$.
  3. $3\hat i+4\hat j$.
  4. Yes.
Section C — Short Answer (3 marks)
  1. $\tfrac17(2\hat i+3\hat j+6\hat k)$.
  2. $\hat i+\hat j+2\hat k$.
  3. $6\hat i+8\hat j$.
  4. $(3,4,5)$.
Section D — Long Answer (5 marks)
  1. $\tfrac{1}{\sqrt2}(\hat i+\hat j)$.
  2. Collinear ($\overrightarrow{AB}\parallel\overrightarrow{BC}$).
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