which one of these statements are true of vector v = (3,4)?

Question

a) lvl = 7
b) k v = (3, -4) given k = -1
c) u + v = (6, 0) given u = (3, 4)
d) if k = 1/5 then kv is a unit vector with the same direction as v.

Answer 1

(d) is correct.

(a) |v| = sqrt(x^2+y^2) = sqrt(9+16) = 5
That's not 7, so (a) is not correct.

(b) kv, given k=-1 is (kx,ky) = (-3, -4)
That's not (3,-4) so (b) is not correct

(c) u+v, given u=(3,4) is (x1+x2,y1+y2) = (3+3,4+4) = (6,8)
That's not (6,0), so (c) is incorrect

(d) kv, given k=1/5 is in the same direction as v (3/5,4/5). To determine it is a unit vector, calculate |kv| which is sqrt((3/5)^2 + (4/5)^2) = sqrt(9/25 + 16/25) = sqrt(1) = 1
So, since kv is in the same direction as v, and |kv| = 1, it is "a unit vector with the same direction as v," and (d) is correct.

Answer 2

D
the magnitude of vector v is 5. ( sq rt of (3^2 + 4^2) ) = 5
the unit vector is the vector divided by the magnitude v/5.
(3/5, 4/5)
which is equal to d) because kv = 1/5 * (3, 4)