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This set of Physics Multiple Choice Questions & Answers (MCQs) focuses on “Vector Addition – Analytical Method”.

1. On adding two vectors we get _____
a) A vector
b) A scalar
c) A number
d) An operation

Explanation: Addition of two vectors gives a vector as the result. The same goes for subtraction and cross multiplication. It is only when two vectors are operated through dot product, we get a scalar as the result.

2. Adding 2î + 7ĵ and î + ĵ gives ______
a) 3î + 8ĵ
b) î + 35ĵ
c) î + 8ĵ
d) 2î + 7ĵ

Explanation: When 2î + 7ĵ is added to î + ĵ, the corresponding components get added. Hence, the answer is 3î + 8ĵ.

3. Subtracting 2î + 7ĵ from î + ĵ gives ______
a) -î – 6ĵ
b) 3î + 8ĵ
c) î + 6ĵ
d) 7ĵ

Explanation: When 2î + 7ĵ is subtracted from î + ĵ, the corresponding components get subtracted. Hence, the answer is -î – 6ĵ.

4. Adding î + 77ĵ and 7î + ĵ gives ______
a) 8î + 78ĵ
b) 0î + 76ĵ
c) î + 74ĵ
d) 78î + 8ĵ

Explanation: When î + 77ĵ is added to 7î + ĵ, the corresponding components get added. Hence, the answer is 8î + 78ĵ.

5. When two vectors in the same direction are added, the magnitude of resulting vector is equal to _______
a) Sum of magnitudes of the vectors
b) Difference of magnitudes of the vectors
c) Product of magnitudes of the vectors
d) Sum of the roots of magnitudes of the vectors

Explanation: Consider the graphical representation of these two vectors. When one vector is added to the other in the same direction, the lengths will be added. The resultant vector will bear the resultant length. Length is the magnitude of the vector. Hence the magnitudes add to give the magnitude of the resultant vector.

6. A vector, 7 units from the origin, along the X axis, is added to vector 11 units from the origin along the Y axis. What is the resultant vector?
a) 3î + 8ĵ
b) 7î + 11ĵ
c) 11î + 7ĵ
d) 2î + 7ĵ

Explanation: The vector 7 units from the origin and along X axis is 7î. The vector 11 units from the origin and along Y axis is 11ĵ. Hence the sum is 7î + 11ĵ.

7. Unit vector along the vector 4î + 3ĵ is _____
a) (4î + 3ĵ)/5
b) 4î + 3ĵ
c) (4î + 3ĵ)/6
d) (4î + 3ĵ)/10

Explanation: Unit vector along 4î + 3ĵ , is obtained by dividing the present vector by its magnitude. The magnitude of the given vector is 5. Hence, the required unit vector is (4î + 3ĵ)/5.

8. Unit vector which is perpendicular to the vector 4î + 3ĵ is _____
a) ĵ
b) î
c) 4î + 3ĵ
d) $$\hat{z}$$

Explanation: The dot product of any two vectors which are perpendicular to each other is 0. The dot product of all the vectors in the options with 4î + 3ĵ is non-zero except for $$\hat{z}$$. Hence $$\hat{z}$$ is perpendicular to the given vector.

9. The vector 40î + 30ĵ is added to a vector. The result gives 15î + 3ĵ as the answer. The unknown vector is _____
a) -25î – 27ĵ
b) 25î + 27ĵ
c) -25î + 27ĵ
d) 25î – 27ĵ

Explanation: The required vector can be obtained by subtracting 40î + 30ĵ from 15î + 3ĵ. The result gives -25î – 27ĵ. One should pay attention on which vector has to be subtracted from which one.

10. Calculating the relative velocity is an example of ______
b) Vector subtraction
c) Vector multiplication
d) Vector division

Explanation: The formula for relative velocity is, Vector VR = Vector VA – Vector VB. Finding relative velocity is an example of vector subtraction. In fact, finding the relative value for any vector quantity, we need to do vector subtraction.

11. A vector, 5 units from the origin, along the X axis, is added to vector 2 units from the origin along the Y axis. What is the resultant vector?
a) 3î + 8ĵ
b) 5î + 2ĵ
c) 2î + 5ĵ
d) 2î + 7ĵ

Explanation: The vector 5 units from the origin and along X axis is 5î. The vector 2 units from the origin and along Y axis is 2ĵ. Hence the sum is 5î + 2ĵ.

12. A vector, 14 units from the origin, along the X axis, is added to vector 16 units from the origin along the Z axis. What is the resultant vector?
a) 3î + 8$$\hat{z}$$
b) 14î + 16$$\hat{z}$$
c) 16î + 14$$\hat{z}$$
d) 2î + 7$$\hat{z}$$

Explanation: The vector 14 units from the origin and along X axis is 14î. The vector 16 units from the origin and along Y axis is 16$$\hat{z}$$. Hence the sum is 14î + 16$$\hat{z}$$. 