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Answer to Question #29443 in Vector Calculus for Akarsh Anupam
Question #29443
The resultant of scalar product and vector product of two given vectors is zero. If one vector is i. What is the other vector??
Expert's answer
If two vectors are collinear, i.e. angle between them is 0,their vector product is 0.
If two vectors are orthogonal, i.e. angle between them is pi/2, their scalar product is 0.
Thus, if one vector is i, the other one is j, k, or any linear combination of j and k, then only the scalar product will be zero.
Thus, if one vector is i, the other one is collinear to i (that is, Ai, where A is a real constant), then only the vector product will be zero.
Thus, if one vector is i, the other one is zero vector, then both the scalar product and the vector product will be zero.
If two vectors are orthogonal, i.e. angle between them is pi/2, their scalar product is 0.
Thus, if one vector is i, the other one is j, k, or any linear combination of j and k, then only the scalar product will be zero.
Thus, if one vector is i, the other one is collinear to i (that is, Ai, where A is a real constant), then only the vector product will be zero.
Thus, if one vector is i, the other one is zero vector, then both the scalar product and the vector product will be zero.
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#340153 on Dec 2023
#340153 on Dec 2023
Comments
Thank you for correcting us.
No the other vector must be a null or zero vector . because if the other vector is "j" or "k" , then the scalar product is 0 ( as cos 90 is 0 ) but the vector product is not 0 ( sine 90 is 1) . and if they are anti parallel or parallel then vector product is 0 but not scalar product . So the other vector must be 0 to make both cross product and dot product 0.
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