You are given vectors a⃗ = 5.5 i^− 6.6 j^ and b⃗ = 3.1 i^+ 7.1 j^. a third vector c⃗ lies in the xy-plane. vector c⃗ is perpendicular to vector a⃗ and the scalar product of c⃗ with b⃗ is 20.0.

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:

Now since we know the scalar product between C and B is 20, we can write another equation:

From the first equation we have that:

And now we can replace the X in the 2nd equation:

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:

step-by-step explanation:

33

step-by-step explanation: g=6