Question 366167
The dot product is distributive.
{{{(a-2b)*(3a+5b)=3a*a+5b*a-6b*a-10b*b}}}
Since the vectors are perpendicular,
{{{a*b=b*a=0}}}
Then,
{{{(a-2b)*(3a+5b)=3a*a-10b*b}}}
.
.
{{{a*a=abs(a)}}}
{{{b*b=abs(b)}}}
So,
{{{highlight((a-2b)*(3a+5b)=3abs(a)-10abs(b))}}}