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If A and B are Two non -zero vector havi...

If A and B are Two non -zero vector having equal magnitude , the angle between the vector A and A-B is

A

`0^(@)`

B

`90^(@)`

C

`180^(@)`

D

dependent on the orientation o fA and B

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The correct Answer is:
To solve the problem of finding the angle between vector A and vector A - B, where A and B are two non-zero vectors of equal magnitude, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding the Vectors**: - Let vector A have a magnitude of |A| and vector B also have a magnitude of |B|. Since they have equal magnitudes, we can write |A| = |B|. 2. **Expressing A - B**: - The vector A - B can be visualized as vector A plus the negative of vector B. This means that if vector B is represented in one direction, vector -B will be in the opposite direction. 3. **Visualizing the Vectors**: - Draw vector A and vector B. Since |A| = |B|, when you draw vector B, you can draw vector -B in the opposite direction from the tail of vector A. 4. **Using the Triangle Law of Vector Addition**: - According to the triangle law, the resultant vector A - B can be represented as a triangle where one side is A and the other side is -B. The resultant vector A - B will be the vector that completes the triangle. 5. **Finding the Angle**: - The angle between vector A and vector A - B (let's call it α) will depend on the angle θ between vectors A and B. The angle α can be calculated using the cosine rule or by understanding that the angle between A and A - B will depend on the orientation of A and B. 6. **Conclusion**: - Since the angle α depends on the angle θ between the vectors A and B, we conclude that the angle between vector A and vector A - B is not fixed. Therefore, the answer is that the angle is dependent on the orientation of vectors A and B. ### Final Answer: The angle between vector A and vector A - B is dependent on the orientation of vectors A and B.
To solve the problem of finding the angle between vector A and vector A - B, where A and B are two non-zero vectors of equal magnitude, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding the Vectors**: - Let vector A have a magnitude of |A| and vector B also have a magnitude of |B|. Since they have equal magnitudes, we can write |A| = |B|. 2. **Expressing A - B**: ...
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