Trigonometry

Question

Use the dot product  to determine whether the vectors are parallel, orthogonal,or neither 

v=3i+2j, w=6i+4j

A. Parallel 

B neither 

C. Orthogonal 

Answer 1

if x is angle between two vector v and w then

 

cos x = v.w / ||v|| ||w||

 

v=3i+2j, w=6i+4j

 

v.w = (3)(6) +(2)(4) = 18+8=26

 

||v|| = sqrt (3² +2² )=sqrt(9+4)=sqrt (13)=3.6

 

||w|| =sqrt(6² +4²) =sqrt(36+16)=sqrt(52)=7.2

 

cos x =26/(3.6)(7.2)=26/26=1

 

x= cos^-1 1 = 0

 

As angle between two lines are 0 they are parallel