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.
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)
All components of the zero vector equal to zero.
When the angle between two vectors is zero ... i.e. the vectors are parallel ... their sum is a vector in thesame direction, and with magnitude equal to the sum of the magnitudes of the two original vectors.
Yes. A vector in two dimensions is broken into two components, a vector in three dimensions broken into three components, etc... If the value of all but one component of a vector equal zero then the magnitude of the vector is equal to the non-zero component.
When b is zero.
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)
All components of the zero vector equal to zero.
When the angle between two vectors is zero ... i.e. the vectors are parallel ... their sum is a vector in thesame direction, and with magnitude equal to the sum of the magnitudes of the two original vectors.
The zero vector, denoted as 0, is a vector with all components equal to zero. It serves as the additive identity element in vector spaces, meaning that adding it to any vector does not change the vector's value.
Yes. A vector in two dimensions is broken into two components, a vector in three dimensions broken into three components, etc... If the value of all but one component of a vector equal zero then the magnitude of the vector is equal to the non-zero component.
The sum of all forces is equal to zero when added using the vector method The sum of all torque is equal to zero when added using the vector method
The direction of the resultant vector with zero magnitude is indeterminate or undefined because the two equal and opposite vectors cancel each other out completely.
Only if one of them has a magnitude of zero, so, effectively, no.
When b is zero.
If any component of a vector is not zero, then the vector is not zero.
Sum of two vectors can only be zero if they are equal in magnitude and opposite in direction. So no two vector of unequal magnitude cannot be added to give null vector. Three vectors of equal magnitude and making an angle 120 degrees with each other gives a zero resultant.
zero