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Which of the following is true?
- a)i x i =1
- b)j x i = -j
- c)k x j = -i
- d)k x k = 1
Correct answer is option 'C'. Can you explain this answer?
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Which of the following is true?a)i x i =1b)j x i = -jc)k x j = -id)k x...
As the mathematic equation for the cross product is having a cosine function in it, in which the angle used in the function is the angle between the vectors. Thus the cross product will be zero if the angle between them is 90.
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Which of the following is true?a)i x i =1b)j x i = -jc)k x j = -id)k x...
The correct answer is option 'C': k x j = -i.
The given question is related to the cross product of vectors in three-dimensional space. In three-dimensional space, the cross product of two vectors results in a third vector that is orthogonal to the original two vectors.
Let's consider the three fundamental unit vectors in three-dimensional space:
i: Represents the unit vector in the x-direction.
j: Represents the unit vector in the y-direction.
k: Represents the unit vector in the z-direction.
To find the cross product of two vectors, we can use the following formula:
A x B = (A2B3 - A3B2)i + (A3B1 - A1B3)j + (A1B2 - A2B1)k
where Ai and Bi are the components of vectors A and B, respectively.
Now, let's calculate the cross product of vectors k and j:
k x j = (k2j3 - k3j2)i + (k3j1 - k1j3)j + (k1j2 - k2j1)k
Since k1 = k2 = k3 = 0 and j1 = j2 = j3 = 0, the above equation simplifies to:
k x j = 0i + 0j + 0k
Therefore, the cross product of k and j is a zero vector, which means it is orthogonal to both k and j.
Hence, option 'C' is the correct answer: k x j = -i.
The given question is related to the cross product of vectors in three-dimensional space. In three-dimensional space, the cross product of two vectors results in a third vector that is orthogonal to the original two vectors.
Let's consider the three fundamental unit vectors in three-dimensional space:
i: Represents the unit vector in the x-direction.
j: Represents the unit vector in the y-direction.
k: Represents the unit vector in the z-direction.
To find the cross product of two vectors, we can use the following formula:
A x B = (A2B3 - A3B2)i + (A3B1 - A1B3)j + (A1B2 - A2B1)k
where Ai and Bi are the components of vectors A and B, respectively.
Now, let's calculate the cross product of vectors k and j:
k x j = (k2j3 - k3j2)i + (k3j1 - k1j3)j + (k1j2 - k2j1)k
Since k1 = k2 = k3 = 0 and j1 = j2 = j3 = 0, the above equation simplifies to:
k x j = 0i + 0j + 0k
Therefore, the cross product of k and j is a zero vector, which means it is orthogonal to both k and j.
Hence, option 'C' is the correct answer: k x j = -i.
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Which of the following is true?a)i x i =1b)j x i = -jc)k x j = -id)k x k = 1Correct answer is option 'C'. Can you explain this answer?
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