Unit vector problem??

Question

If A = a(2.0i, 8.0j), where a is a constant, determine the value of a that makes A a unit vector.

I'm very confused and the book is no help.

Can you show me how you got the answer?

Thanks!

Answer 1

A = 2a i + 8a j

Magnitude of A = sqrt.[(2a)^2 + (8a)^2]

Since A is a unit vector, magnitude of A is equal to 1.

So

sqrt.[(2a)^2 + (8a)^2] = 1

Solve of a :

a = 1/sqrt(68)

Hope this helps.

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