It is possible for a vector to be zero if a component of the vector is not zero?

Answer 1

No. The value of a vector is determined by the square root of the sum of its components squared. Value= Sqrt(x^2 + y^2 + z^2). The components of real vectors are real numbers and the square of a real number is a positive number. The sum of a positive and zeros is not zero but a positive.

Vectors were created by William Rowan Hamilton in 1843 when he created Quaternions. Quaternions consist of a real number and three vector numbers. The vectors are designated by i, j, k where i^2=j^2=k^2=ijk= -1. The square of a vector is a negative one . This used to be called an imaginary number. The components of vectors are real numbers, like v=2i + 3j -5k, the value of v = sqrt(4 + 9 + 25)=sqrt(38).

Complex numbers are a subset of quaternions involving one vector "i".

Answer 2

Not necessarily.

As long as one component vector is not zero, the vector will not be zero. The component vector in the j direction could be zero, but if the component vector in the i direction is +4N, then the vector is +4Ni or +4N E. If a component vector is 0, that just means that there is no motion in that direction. The motion only occurs on a different plane.

Answer 3

Yes it possible because if the vector is lying horizontally on the X-axis, it has one component to be the X axis, but the other component is zero, due to the Y-axis being zero.

Answer 4

yes. specially when the components have same length but in different direction

Answer 5

The component perpendicular to the direction of the vector is always zero,

but that doesn't mean that the vector is always zero.

Answer 6

No. At least, if you consider the standard vectors in Rn space, often used in physics, their length (or magnitude) must always be greater than or equal to any of its components.

Answer 7

No. The magnitude of a vector can't be less than either of its components.

Answer 8

yes

Answer 9

no