If vector a = 2i - j + 2k and vector b = -i + j - k then find a unit v

1.	If vector a = 2i - j + 2k and vector b = -i + j - k then find a unit vector in the direction of vector(a + b).
Answer» Here, vector a = 2i - j + 2k and vector b = -i + j - k ∴ vector(a + b) = i + 0, j + k = i + k ∴ vector\|a + b\| = √(1² + 0² + 1²) = √2 So, unit vector in the direction of vector(a + b) = vector((a + b)/\|a + b\|) = (i + k)/√2 = (1/√2)i + (1/2)j

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

Answer»

Here, vector a = 2i - j + 2k

and vector b = -i + j - k

∴ vector(a + b) = i + 0, j + k = i + k

∴ vector|a + b| = √(1² + 0² + 1²) = √2

So, unit vector in the direction of

vector(a + b) = vector((a + b)/|a + b|) = (i + k)/√2

= (1/√2)i + (1/2)j