- In order to add two vectors :
their components have to positive

they have to have equal number of components

the components of the 2nd vector must be positive

- The product of a scalar and a vector is :
a scalar

a vector perpendicular to the original vector

a vector of unknown direction

a vector aligned with the original vector

- You multiply a vector by a scalar :
multiply only the x-component by the scalar

multiply each component by the scalar

do nothing

- When you multiply a vector by the inverse of its magnitude the
resulting vector :
has the magnitude of 1 (one) and points in opposite direction

has unknown magnitude and points in the same direction

has the magnitude of 1 (one) and points in the same direction

has unknown magnitude and points in the same direction

as the original vector.

- The result of the dot-product of two vectors is :
a scalar always positive

a scalar never zero

always zero if the x-component of the vector is zero

only zero if the scalar is zero

a scalar either positive,negative or zero

- The result of the dot-product of two non-zero vectors is :
never zero

zero only if the two vectors point in opposite direction

zero only if the two vectors point in the same direction

zero only if the two vectors are perpendicular to each other

- The result of the dot-product of a vector with itself :
equal to the unit vector

is always zero

is equal to the magnitude squared of the vector

is equal to the magnitude of the vector

- The cross-product of two vectors is :
only zero if the first vector is zero

only zero if the second vector is zero

zero if both vectors are aligned.

- The cross-product of two vectors is :
is a scalar

is a vector of unknown direction

is a vector perpendicular to the first vector but arbitrary
otherwise

is a vector perpendicular to both given vectors

is a vector perpendicular to the second vector but arbitrary
otherwise

is a vector of unknow direction

- For given vectors
and
the two cross products
x
and
x
produce two new vectors. These two new vectors
are mutually perpendicular to each other

are identical in magnitude and direction

are identical in magnitude but opposite in direction

have nothing to do with each other

- The cross-product of a vector with itself :
is a scalar

is a vector of zero magnitude

cannot be calculated

is a vector perpendicular to the given vector