Question

# The component of vector ( 6hat{i}-3hat{j}-6hat{k}) parallel to the vector (hat{i} +hat{j}+hat{k}).

Solution

Let the vector 11 to (hat{i} + hat{j} + hat{k})

= (lambda) (hat{i} + hat{j} + hat{k})

( therefore ) comp aloy ( =lambda (hat{i}+hat{f}+hat{t}) )

[

begin{array}{l}

=frac{left.(6hat{i}-3hat{j}-6 hat{k}) cdot(hat{i}+hat{j}+hat{k})^{}right)}{(sqrt{1^{2}+1^{2}+1^{2}})^{}}

=frac{6-3-6}{sqrt{3}}

=-3 / sqrt{3}

-sqrt{3}

end{array}

]