determine whether u and v are orthogonal, parallel or neither.
u= (4,7)
v= (-28,8)
If the coordinates of u and v represent the heads of vectors that start at the origin, then the slope of u = 7/4 and the slope of v = -8/28 → -2/7
The slopes are not the same hence the lines are not parallel.
The slope of v is not -1/the slope of u, hence the lines are not orthogonal.
Good evening Guest!
determine whether u and v are orthogonal, parallel or neither.
u= (4,7)
v= (-28,8)
The slope of the function through the points u and v is
The connection line u - v is not perpendicular or parallel to the abscissa axis of the Cartesian coordinate system.
The slope to the abscissa is
Greeting asinus :- )
!
If the coordinates of u and v represent the heads of vectors that start at the origin, then the slope of u = 7/4 and the slope of v = -8/28 → -2/7
The slopes are not the same hence the lines are not parallel.
The slope of v is not -1/the slope of u, hence the lines are not orthogonal.
The vectors will be orthogonal if their dot product = 0 .....so we have
u (dot) v =
4 * -28 + 7 * 8 =
-112 + 56 =
-56 ...so they are not orthogonal
They will be parallel when either
u (dot) v = ll u ll * ll v ll or
u (dot) v = - ll u ll * ll v ll
ll u ll = √ [ 4^2 + 7^2] = √ 65 and ll v ll = √ [ 28^2 + 8^2] = √ 848
So - ll u ll * ll v ll = - √ 65 * √ 848 = -√55120 = about - 238.78 so.....this does not equal the dot product, so they are not parallel, either