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Which of the following statements is not true regarding vector algebra?
- a)Dot product of iike unit vector is unity
- b)Dot product of unlike unit vector is zero
- c)Cross product of two like unit vectors is a third unit vector having positive sign for normal rotation and negative for reverse rotation.
- d)All the above statements are true
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Which of the following statements is not true regarding vector algebra...
Option (c) is not correct because cross product of two unlike vectors is a third unit vector having positive sign for normal rotation and negative for reverse rotation while cross product of two like unit vectors is zero.
Most Upvoted Answer
Which of the following statements is not true regarding vector algebra...
Explanation:
In vector algebra, we have several operations such as addition, subtraction, dot product, and cross product. Let's analyze each statement to determine which one is not true.
Statement a: Dot product of like unit vector is unity.
- This statement is true. When we take the dot product of two like unit vectors (for example, i.i, j.j, or k.k), the result is always 1. This is because the dot product of two unit vectors measures the cosine of the angle between them, and for like unit vectors, the angle is 0 degrees, so cos(0) = 1.
Statement b: Dot product of unlike unit vector is zero.
- This statement is also true. When we take the dot product of two unlike unit vectors (for example, i.j, i.k, or j.k), the result is always 0. This is because the dot product of two unit vectors measures the cosine of the angle between them, and for unlike unit vectors, the angle is 90 degrees, so cos(90) = 0.
Statement c: Cross product of two like unit vectors is a third unit vector having positive sign for normal rotation and negative for reverse rotation.
- This statement is not true. The cross product of two like unit vectors (for example, i x i, j x j, or k x k) is always the zero vector, not a third unit vector. This is because the cross product of two parallel vectors is always zero.
Therefore, the correct answer is option 'C' because the statement it describes is not true. The cross product of two like unit vectors does not result in a third unit vector; it results in the zero vector.
In vector algebra, we have several operations such as addition, subtraction, dot product, and cross product. Let's analyze each statement to determine which one is not true.
Statement a: Dot product of like unit vector is unity.
- This statement is true. When we take the dot product of two like unit vectors (for example, i.i, j.j, or k.k), the result is always 1. This is because the dot product of two unit vectors measures the cosine of the angle between them, and for like unit vectors, the angle is 0 degrees, so cos(0) = 1.
Statement b: Dot product of unlike unit vector is zero.
- This statement is also true. When we take the dot product of two unlike unit vectors (for example, i.j, i.k, or j.k), the result is always 0. This is because the dot product of two unit vectors measures the cosine of the angle between them, and for unlike unit vectors, the angle is 90 degrees, so cos(90) = 0.
Statement c: Cross product of two like unit vectors is a third unit vector having positive sign for normal rotation and negative for reverse rotation.
- This statement is not true. The cross product of two like unit vectors (for example, i x i, j x j, or k x k) is always the zero vector, not a third unit vector. This is because the cross product of two parallel vectors is always zero.
Therefore, the correct answer is option 'C' because the statement it describes is not true. The cross product of two like unit vectors does not result in a third unit vector; it results in the zero vector.
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Which of the following statements is not true regarding vector algebra?a)Dot product of iike unit vector is unityb)Dot product of unlike unit vector is zeroc)Cross product of two like unit vectors is a third unit vector having positive sign for normal rotation and negative for reverse rotation.d)All the above statements are trueCorrect answer is option 'C'. Can you explain this answer?
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