# Physics Questions and Answers – Motion in a Plane – Multiplication of Vectors by Real Numbers

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This set of Physics Questions and Answers for Entrance exams focuses on “Motion in a Plane – Multiplication of Vectors by Real Numbers”.

1. Multiplying 2î + 7ĵ by 5 gives ______
a) 10î + 35ĵ
b) 2î + 35ĵ
c) 10î + 7ĵ
d) 2î + 7ĵ

Explanation: When 2î + 7ĵ is multiplied by 5, both the components get multiplied by 5. Hence, the answer is 10î + 35ĵ.

2. Dividing 5î + 10ĵ by 5 gives ______
a) î + 2ĵ
b) î + 4ĵ
c) î + ĵ
d) 2î + ĵ,

Explanation: When 5î + 10ĵ is divided by 5, both the components get divided by 5. Hence, the answer is î + 2ĵ.

3. Eleven times unit vector along X added to 7 times unit vector along Y gives ______
a) 11î + 7ĵ
b) 7î + 11ĵ
c) 7î + 7ĵ
d) 11î + 11ĵ

Explanation: Unit vector along X is î and that along Y is ĵ. Hence, eleven times unit vector along X added to 7 times unit vector along Y will give 11î + 7ĵ.
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4. A unit vector has the magnitude of ___
a) 5
b) 1
c) 10
d) 0

Explanation: A unit vector has the magnitude 1. It is used to represent non-unit vectors using along other unit vectors. Any vector can be represented as a sum of unit vectors, multiplied by required scalars.

5. What happens when a vector is multiplied by a scalar?
a) Its magnitude gets multiplied by that much amount
b) Its direction rotates in XY plane by that much angle
c) Its direction rotates in YZ plane by that much angle
d) Its direction rotates in ZX plane by that much angle

Explanation: Any vector a, can be written as a = |a|($$\widehat{unit vector}$$). Hence, when we multiply it by a scalar, the magnitude multiplies by that much amount.

6. A car travels 5m in X direction and then 7m in Y direction. What is the final vector position of the car with respect to the origin?
a) 5î + 7ĵ
b) 7î + 5ĵ
c) 7î + 7ĵ
d) 5î + 5ĵ

Explanation: Unit vector along X is î and that along Y is ĵ. Hence, when the car travels 5m in X direction and 7m in y direction, the final position becomes 5î + 7ĵ.

7. What is the result when î + 14ĵ is multiplied by √49?
a) 7î + 98ĵ
b) 98î + 14ĵ
c) 7î + 98ĵ
d) (î + 7ĵ)*√49

Explanation: $$\sqrt{49}$$ = 7. When î + 14ĵ is multiplied by 7, we get 7î + 98ĵ as the answer. Hence, 7î + 98ĵ is the correct answer.

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