Resolution of Vectors and Vector Operations - Worksheet

 

Worksheet: Resolution of Vectors & Vector Operations (JEE Main / NEET Level)

Topics Covered

• Resolution of vectors
• Rectangular components
• Unit vectors
• $\hat{i}, \hat{j}, \hat{k}$ notation
• Vector addition
• Scalar multiplication
• Magnitude of vectors
• Direction cosines (basic)
• Position vectors

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Instructions

• Total Questions: 20
• Type: Multiple Choice Questions (MCQs)
• Difficulty: JEE Main / NEET
• Assume standard Cartesian coordinate system.

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Questions

1. A vector of magnitude 20 N makes an angle of 30° with the positive x-axis. Its x-component is

A) 10 N

B) $10\sqrt3$ N

C) 20 N

D) $20\sqrt3$ N

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2. A vector has components 

$6\hat i+8\hat j$. Its magnitude is

A) 8

B) 10

C) 12

D) 14

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3. The unit vector along the positive y-axis is

A) $\hat i$

B) $\hat j$

C) $\hat k$

D) $-\hat j$

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4. The vector 

$5\hat i-12\hat j$ has magnitude

A) 12

B) 13

C) 15

D) 17

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5. If 

$\vec A=2\hat i+3\hat j$ and $\vec B=4\hat i-\hat j$, then $\vec A+\vec B$ is

A) $6\hat i+2\hat j$

B) $2\hat i+2\hat j$

C) $6\hat i-2\hat j$

D) $4\hat i+4\hat j$

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6. The vector 

$3(2\hat i-\hat j+4\hat k)$ equals

A) $6\hat i-3\hat j+12\hat k$

B) $5\hat i-3\hat j+4\hat k$

C) $2\hat i-\hat j+12\hat k$

D) $3\hat i-3\hat j+12\hat k$

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7. The magnitude of the unit vector is

A) 0

B) 1

C) Depends on direction

D) Infinite

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8. A force of 50 N acts at 53° to the horizontal. Its vertical component is

A) 20 N

B) 30 N

C) 40 N

D) 50 N

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9. If 

$\vec A=3\hat i+4\hat j$, then the corresponding unit vector is

A) $\dfrac35\hat i+\dfrac45\hat j$

B) $\dfrac45\hat i+\dfrac35\hat j$

C) $5\hat i+5\hat j$

D) $3\hat i+4\hat j$

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10. Which of the following is a unit vector?

A) $2\hat i$

B) $\hat i+\hat j$

C) $\hat k$

D) $2\hat j-2\hat k$

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11. The vector joining the origin to the point (4, –2, 5) is

A) $4\hat i+2\hat j+5\hat k$

B) $4\hat i-2\hat j+5\hat k$

C) $4\hat i-2\hat j-5\hat k$

D) $-4\hat i+2\hat j+5\hat k$

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12. The magnitude of 

$2\hat i+3\hat j+6\hat k$ is

A) 7

B) 8

C) 9

D) 10

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13. 

If $\vec A=5\hat i+2\hat j$, then $2\vec A$ equals

A) $5\hat i+4\hat j$

B) $10\hat i+4\hat j$

C) $10\hat i+2\hat j$

D) $5\hat i+2\hat j$

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14. The x-component of the vector 

$12\hat i-5\hat j+9\hat k$ is

A) 5

B) 9

C) 12

D) 26

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15. A vector has components (8, 6). The angle it makes with the positive x-axis is

A) $30^\circ$

B) $37^\circ$

C) $45^\circ$

D) $60^\circ$

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16. If

$$\vec A=\hat i+2\hat j-\hat k,\qquad \vec B=3\hat i-\hat j+4\hat k$$

then $\vec A+\vec B$ equals

A) $4\hat i+\hat j+3\hat k$

B) $2\hat i+\hat j+5\hat k$

C) $4\hat i-\hat j+3\hat k$

D) $2\hat i-\hat j+5\hat k$

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17. Which of the following represents a vector parallel to

$$2\hat i-4\hat j+6\hat k$$

A) $\hat i-2\hat j+3\hat k$

B) $2\hat i+4\hat j+6\hat k$

C) $4\hat i-6\hat j+8\hat k$

D) $3\hat i-4\hat j+6\hat k$

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18. The resultant of

$$4\hat i+3\hat j$$

and 

$$-4\hat i+5\hat j$$

is

A) $8\hat j$

B) $2\hat j$

C) $7\hat j$

D) $4\hat i+8\hat j$

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19.

A vector of magnitude 10 acts at 60° above the x-axis. Its components are

A) $5\hat i+5\sqrt3\hat j$

B) $5\sqrt3\hat i+5\hat j$

C) $10\hat i$

D) $10\hat j$

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20. The vector

$$3\hat i-4\hat j+12\hat k$$

has magnitude

A) 11

B) 12

C) 13

D) 15

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Answer Key

Q	Ans
1	B
2	B
3	B
4	B
5	A
6	A
7	B
8	C
9	A
10	C
11	B
12	A
13	B
14	C
15	B
16	A
17	A
18	A
19	A
20	C