Calculate A, Distance, & Position Vector of T & S

[salman213]

1. Given A = x^2y.ax — yz.ay + yz^2.az, determine:
(a) The magnitude of A at point T(2, -1,3)
(b) The distance vector from T to 5 if S is 5.6 units away from T and in the same direction
as A at T
(c) The position vector of S



3.

(a) well for this one just plug in the point T, and solve for A.


(b) How do i calculate this point :S?


(c) well once i find the points S then i can just take that point from the origin to it and that's the position vector. I am just confused about b.

 

[Defennder]

b) A vector is entirely determined by its magnitude and direction. You are given he magnitude, and you're told the direction, though indirectly. So what you need to do is to figure out the direction by normalising what you are given ie. make it of magnitude 1. Then you should see what to do next.

c)Follows from b.

 

[salman213]

so basically the direction that b refers to is the direction of the distance vector it is asking about. The direction is not of the position vector s? (originally i though the position vector s was in the direction of a)...

 

[Defennder]

so basically the direction that b refers to is the direction of the distance vector it is asking about. The direction is not of the position vector s?

Yes you're right. The latter statement is mistaken.

(originally i though the position vector s was in the direction of a)...

Don't see where you got that from. Remember that A isn't a vector but a vector function, which means it gives you a direction after you input the coordinate values.