# Thread: Find vectors b1 and b2

1. ## Find vectors b1 and b2

Two vectors a = 2i - 2j +k and b = 2i + j - k are given. Write the vector b as sum of vectors $\mathbf{b_1}$ and $\mathbf{b_2}$ such that $\mathbf{b_1}$ is parallel to a and $\mathbf{b_2}$ is perpendicular to a.Find the vectors $\mathbf{b_1}$ and $\mathbf{b_2}$

2. Originally Posted by varunnayudu
Two vectors a = 2i - 2j +k and b = 2i + j - k are given. Write the vector b as sum of vectors $\mathbf{b_1}$ and $\mathbf{b_2}$ such that $\mathbf{b_1}$ is parallel to a and $\mathbf{b_2}$ is perpendicular to a.Find the vectors $\mathbf{b_1}$ and $\mathbf{b_2}$
b = b1 + b2

Well b1 is parallel to a is the same as saying b1 = za.
b2
is perpendicular to a is same as saying b2 . a = 0.

From b = b1 + b2 we get, b.a = b1 . a = z |a|^2 you can get z and thus b1.

Then you can get b2 by b - b1.

Get it?