Determine whether u and v are orthogonal, parallel or neither
u= <-4, 7>, v= <-14, 12>
To determine whether two vectors u and v are orthogonal, parallel, or neither, we can use the dot product.
The dot product of two vectors u = <-4, 7> and v = <-14, 12> can be calculated as follows:
u ยท v = (-4 * -14) + (7 * 12)
= 56 + 84
= 140
If the dot product is zero, then the vectors u and v are orthogonal. If the dot product is a non-zero scalar multiple, then the vectors u and v are parallel. If the dot product is neither zero nor a scalar multiple, then the vectors u and v are neither orthogonal nor parallel.
In this case, the dot product of u and v is 140, which is not zero. Therefore, u and v are not orthogonal. Since the dot product is not a scalar multiple of one another, they are not parallel either. Hence, u and v neither orthogonal nor parallel.