If vector a = i + j + 2k and vector b = 2i + j - 2k, find the unit vector in the direction of 2 vector a - vector b.

Question

If \(\vec a = \hat i + \hat j + 2 \hat k\) and \(\vec b = 2 \hat i + \hat j - 2 \hat k\), find the unit vector in the direction of \(2\vec a - \vec b.\)

Answer 1

We need to find the unit vector in the direction of \(2\vec a - \vec b.\).

First, let us calculate \(2\vec a - \vec b.\)

We can easily multiply vector by a scalar by multiplying similar components, that is, vector’s magnitude by the scalar’s magnitude.

We know that, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.

To find a unit vector with the same direction as a given vector, we divide by the magnitude of the vector.

For finding unit vector, we have the formula:

Now we know the value of \(2\vec a - \vec b.\), so we just need to substitute in the above equation.