The zero vector is not perpendicular to all vectors, but it is orthogonal to all vectors.
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That is not even true!
The zero vector is both parallel and perpendicular to any other vector. V.0 = 0 means zero vector is perpendicular to V and Vx0 = 0 means zero vector is parallel to V.
Ans :The Projections Of A Vector And Vector Components Can Be Equal If And Only If The Axes Are Perpendicular .
Yes.
No, the curl of a vector field is a vector field itself and is not required to be perpendicular to every vector field f. The curl is related to the local rotation of the vector field, not its orthogonality to other vector fields.
"Perpendicular " is a relationship, not a vector. Any vector can be perpendicular to any other vector if their angle relationship is an odd multiple of 90 degrees.
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cross product of tow vector result in a vector which is perpendicular the multiplying vector then these three vector are perpedicular
The component of a vector x perpendicular to the vector y is x*y*sin(A) where A is the angle between the two vectors.
That is not even true!
The zero vector is both parallel and perpendicular to any other vector. V.0 = 0 means zero vector is perpendicular to V and Vx0 = 0 means zero vector is parallel to V.
Ans :The Projections Of A Vector And Vector Components Can Be Equal If And Only If The Axes Are Perpendicular .
Yes.
Their directions are perpendicular.
The vorticity vector is DelxV = v/r sin(RV)H1, the Curl of the vector V. The unit vector H1, is perpendicular to the plane formed by the radius vector R and and the vector V.
I think you meant to ask for finding a perpendicular vector, rather than parallel. If that is the case, the cross product of two non-parallel vectors will produce a vector which is perpendicular to both of them, unless they are parallel, which the cross product = 0. (a zero vector)