Trigonometry Study Guide? Help please?

Question

7. Use the given vectors to find the specified scalar u=-4i+4j and v= -11i-6j find U*V

8. Use the dot product to determine whether the vectors are parallel, orthogonal, or neither v=4i+3j, w=3i-4j

Answer 1

7.

The two sclars u and v

u = 4i + 4j and v = -11i - 6j

The product of scalars u and v are

u*v = (4i + 4j)(-11i - 6j)

      =(-44i.i - 24j.j)

     =(-44i - 24j)

 

Comments

The vectors u = -4i + 4j and v = - 11i - 6j

The scalar product of vectors u and v are

u*v = (- 4i + 4j)(-11i - 6j)

     = (- 4)(-11) + (4)(-6)

      =   44 - 24

u*v = 20

Answer 2

8.

The two sclars v and w

v = 4i + 3j and w = 3i - 4j

The product of scalars v and w are

v*w = (4i +3j)(3i - 4j)

      =(12 - 12)

     =0.

The two vectors product is zero therefore the vectors are orthogonal.