if the vector of A = a(3.0i^ + 4.0j^) then what value of "a" will make this a unit vector (a is constant )

Question

if the vector of A = a(3.0i^ + 4.0j^) then what value of "a" will make this a unit vector (a is constant )
the hats belong on the i and j but i couldnt find those characters together. also A should have a vector notation above it but also i couldnt find that character.

Answer 1

a = 1/norm(3.0i + 4j) = 1 / sqrt(3^2 + 4^2) = 1/5.

That way, the length of the vector = a(norm) = 5(1/5) =1, so it is a unit vector.

Answer 2

A unit vector has a length of 1 unit.

The length of your vector A equals the length of the hypotenuse of a triangle with sides 3.0*a and 4.0*a.

Therefore, we know (3a)^2 + (4a)^2 = 1^2
so 25a^2 = 1
so a^2 = 1/25
And therefore, a = 1/5, or 0.2

Hopefully that helps!

Answer 3

If A is a unit vector its length must be one unit. so
sqrt(a^2(9+16))=1
a^2=1/25
a=+1/5or -1/5