Answer:
C=2.22 i^ + 1.85 j^
Step-by-step explanation:
If vector C is perpendicular to vector A, that means the scalar product between C and A is 0, so if C= X i^ + Y j^, using the scalar product definition we can write an equation:
[tex]5.5X - 6.6Y = 0[/tex]
Now since we know the scalar product between C and B is 20, we can write another equation:
[tex]3.1X + 7.1Y = 20[/tex]
From the first equation we have that:
[tex]X = 6.6Y/5.5[/tex]
And now we can replace the X in the 2nd equation:
[tex]3.1 (6.6Y/5.5) + 7.1Y=20[/tex]
Solving, we have that Y=1.85, and using this value we can find X=2.22. You can confirm that C is correctly since:
[tex]5.5*2.22 - 6.6*1.85 = 0[/tex]
[tex]3.1*2.22 + 7.1*1.85 = 20[/tex]
