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Vector Component

Which of the ...

Question

Which of the following quantities is dependent of the choice of orientation of the coordinate axes?

A

\to A

+

\to B

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B

A_{x} + B_{y}

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C

|

\to A

+

\to B

|

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D

Angle between

\to A

and

\to B

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Solution

The correct option is B $A_{x} + B_{y}$
A vector, its magnitude and the angle between two vectors do not depend on the choice of the orientation of the coordinate axes. So $\to A$ + $\to B$ , | $\to A$ + $\to B$ |, angle between A and $\to B$ are independent of the orientation of the coordinate axes.But the quantity $A_{x} + B_{y}$ depends upon the magnitude of the components along x and y axes, so it will change with change in coordinate axes.

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Similar questions

∣ ∣ \to A - \to B ∣ ∣ = ∣ ∣ \to A ∣ ∣ = ∣ ∣ \to B ∣ ∣

, the angle between

\to A

\to B

If $| \to A - \to B | = | \to A | = | \to B |,$ the angle between \( \vec{A}\) and $\to B$

\to a

\to b

are unequal vectors such that

(\to a - \to b) \times [(\to b + \to a) \times (2 \to a + \to b)] = \to a + \to b

, then the angle

θ

\to a

\to b

Q. Cosine of an angle between the vectors

\to a + \to b

\to a - \to b

| \to a | = 2, ∣ ∣ \to b ∣ ∣ = 1

\to a \land \to b = 60^{o}

| \to a + \to b | > | \to a - \to b |

then the angle between

\to a

\to b

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