Question

Determine whether the vectors u and v are parallel, orthogonal, or neither.

u = <6, 4>, v = <-9, 8>

Answer 1

Neither

Explanation:

Given: The given vectors are
`u=<6, 4>` and
`v=<-9, 8>`.

To find: To find whether the vectors u and v are parallel, orthogonal, or neither

Solution: Two vectors are said to be orthogonal if they are perpendicular to each other that is the dot product of the two vectors is zero.

Let us consider the dot product of the vectors

`u{\cdot}v=<6,4>{\cdot}<-9, 8>`

`u{\cdot}v=<6{*}-9, 4{*}8>`

`u{\cdot}v=<-54, 32>`

which is not equal to zero.

Hence, the given vectors are not orthogonal.

Two vectors are said to be parallel if one vector is a scalar multiple of the other vector.

In the given vectors, it can be observed that , one vector can not be expressed as the scalar multiple of the other vector.

Hence, the given vectors are neither parallel nor orthogonal.

Answer 2

The given vectors are
`<6,4>` and
`<-9,8>`

Two vectors are said to be orthogonal if they are perpendicular to each other. i.e. the dot product of the two vectors is zero.

Let us consider the dot product of the vectors

`<6,4>.<-9,8> =<6* -9,4* 8>=<-54,32>` which is not equal to zero. Hence, the given vectors are not orthogonal.

Two vectors are said to be parallel if one vector is a scalar multiple of the other vector.

Here we can observe that the from the given vectors, one vector can not be expressed as the scalar multiple of the other vector.

Hence, the given vectors are neither parallel nor orthogonal.