How would one solve this problem?

Use the dot product to determine whether the vectors are parallel, orthogonal, or neither. $$v = ^\sqrt{2} j, w = 4i$$

A. orthogonal
B. parallel
C. neither

Question

How would one solve this problem?

Use the dot product to determine whether the vectors are parallel, orthogonal, or neither. $$v = ^\sqrt{2} j, w = 4i$$

  A. orthogonal 	
  B. parallel 	
  C. neither

ganeshie8 · Answer

$\large  v = 0i + \sqrt{2} j$
$\large  w = 4i + 0j$

ganeshie8 · Answer

knw how to take the dot product, given two vectors ?

anonymous · Answer

Unfortunately, no... How do I do that though?

ganeshie8 · Answer

multiply the i componnets
multiply the j components

add them both

ganeshie8 · Answer

$\large  v = 0i + \sqrt{2} j$
$\large  w = 4i + 0 j$

$\large   v.w =  0*4 + \sqrt{2}*0  = 0+ 0 = 0$

ganeshie8 · Answer

since the dot product is 0, the vectors will be perpendicular

ganeshie8 · Answer

another name for perpendicular is orthogonal

ganeshie8 · Answer

see if that makes more or less sense...

anonymous · Answer

May I ask what would make the vectors parallel?

ganeshie8 · Answer

the fancy way of saying it is :
the vectors are parallel when the ratio of components are proportional

ganeshie8 · Answer

$\large  v = a_1i + b_1 j$
$\large  w = a_2i + b_2 j$

are parallel if   

$$\large \dfrac{a_1}{a_2} = \dfrac{b_1}{b_2}$$

anonymous · Answer

Thank you very much ^-^