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Q. The vector $b = 3j + 4k$ is to be written as the sum of a vector $b_1$ parallel to $a = i +j$ and a vector $b_2$ perpendicular to $a$. Then $b_1$ is equal to

VITEEEVITEEE 2013Vector Algebra

Solution:

Since, $b _{1} \| a$, therefore $b _{1}-a( i + j )$
$b _{2}= b - b _{1}=(3-a) i -a j +4 k$
Also, $b _{2} \cdot a =0$
$\Rightarrow (3-a)-a \Rightarrow a=\frac{3}{2}$
Hence, $b _{1}=\frac{3}{2}( i + j )$