Magnitude Direction and Operation of Vectors?

Question

What is a magnitude and direction of the following vectors: A(2,1,-4) and B(4,1,1)? Determine the following operations: A+B, A-B, 4(A+B).

Some one please help.

Answer 1

The magnitude of a vector in three dimensions is given by:

(vi² + vj² + vk²)^(1/2)

The direction of the vector is based upon the angle the vector makes with the x, y, and z-axis.

Vector operations are very easy.

A+B = <A1+B1, A2+B2, A3+B3>

A-B = <A1-B1, A2-B2, A3-B3>

4(A+B) = <4(A1+B1), 4(A2+B2), 4(A3+B3)>

Answer 2

The magnitudes are √(21) for A and √(18) = 3√(2) for B.

One way to indicate direction is to give a unit vector in terms of unit vectors in the x, y and z directions, i, j and k respectively.

The unit vector in the direction of A is (2i -j -4k)/√(21)

or (2/√(21))i - (1/√(21))j -(4/√(21))k.

The unit vector in the direction of B is (4i + j +K)/(3√(2)).

Your sums are correct.