How Do I Find Scalars, Unit Vector, and Direction of Resultant Vectors?

[Amil]

A=6i-8j m, B= -8i=3j m

I know how to add and multiply vectors, but how do I find the two scalars of a and b?
Also, I can’t figure out how to find the unit vector and direction of Resultant Vectors.

Please Help!

Thanks

Amil

 

[K.J.Healey]

The "scalar" of a vector I assume you're speaking of the "magnitude" as expressed by the notation |A|. This is similar to finding like the hypotenuse of a triangle.
For A, if you go 6 units to the right, then 8 units down, how far is your point from the origin? Thats what the magnitude is. If you know basic trig you use the pathagorean theorem to solve for that length.

A unit vector is just a vector with a magnitude of 1. So it has the same direction as the original vector, which means it has the same ratio of height to width(i to j). How do you think you could get this vector with magnitude of 1?

"Reslutant" vector I assume you mean that if you do one and then the other from that point, where are you? So it would be basic "vector addition". If your vectors were just 5i and 19i, and you wanted the resultant, well, take a pencil from the origin 0, and move to the right 5 units, then again 19 units. Now a vector is "how far" and "in what direction". So you would be 5+19 = 24 units, still in the "i" direction, so the resultant = 24i. You can apply this same reasoning to the other vectors.

 

[M98Ranger]

Hi Amil,

To find the scalars of a and b, you can use the formula a = ||A||cosθ and b = ||B||cosθ, where ||A|| and ||B|| are the magnitudes of the vectors A and B, and θ is the angle between the vectors.

To find the unit vector of a resultant vector, you can divide the vector by its magnitude. For example, if the resultant vector is C = 10i + 5j, the unit vector would be C/||C|| = (10i + 5j)/√(10^2 + 5^2).

To find the direction of a resultant vector, you can use the formula tanθ = (y/x), where x and y are the components of the vector. This will give you the angle θ in the appropriate quadrant.

I hope this helps! Let me know if you have any further questions or need clarification. Good luck!