Three points exist with ⃗⃗⃗⃗⃗AB= 2i+j and ⃗⃗⃗⃗⃗BC= 2i+5j find angle ABC

The angle between AB and BC= 41,63°

Step-by-step explanation:

Two vectors are given.

Sometimes it helps if you change the j for x and the i for y.

AB= 2y + x

2y + x = 0

2y = -x

y = - 1/2x

BC= 2y + 5x

2y + 5x = 0

2y = -5x

y = - 5/2x

Both lines AB and BC intersect in point (0,0)

The angle between AB and BC can be constructed in a graph.

y = - 1/2x

y = - 5/2x

Measureing the angle between the lines gives you an estimate of the angle. I measured 43°. See the attachment.

The angle of a line with the x-axis, is mathematically the same as the incline or gradient of the line, which is the same as the tan of Alpha.

AB has a gradient of - 1/2

So tan(Alpha) = - 1/2

there fore Alpha = arctan( - 1/2 ) = -26,6 °

BC haa a gradient of - 52

So tan(Beta) = - 5/2

there fore Beta = arctan( - 5/2 ) = -86,2°

Angle between AB and BC

-86,2 - -26,6

-86,2 + 26,6

-41,6°

That corner is the same as 41,6°

The angle between AB and BC= 41,6°

idek

step-by-step explanation: