Question

Determine whether the vectors u and v are parallel, orthogonal, or neither.

u = <7, 2>, v = <21, 6>

Answer 1

Parallel

Explanation:

orthogonal: dot product of u times v= 0 degrees

utimesv= 7x21+2x6=147+12=159

Parallel: cos (u,v)=1

cos (u,v)=(u·v)/ IuI·IvI

cos (u,v)= 159/ (sqrt 7^2+2^2)·(sqrt 21^2 +6^2)

159/(sqrt 49+4) ·(sqrt 441+36)

159/(sqrt 53)·(sqrt 477)=

159/159

=1; therefore it is parallel

Answer 2

Vectors are orthogonal if their dot product is equal to zero:
u · v = 7· 21 + 2 · 6 = 147 + 12 = 159 ≠ 0
Vectors are parallel if the angle between them is 0°, or cos ( u, v ) = 1
cos ( u, v ) = ( u · v ) / ( | u | · | v | ) =
= 159 / (√(7² + 2²) · √(21² + 6²) ) =
= 159 / ( √ (49 + 4 ) · √ ( 441 + 36 ) ) =
= 159 / (√53 · √477 ) = 159 / 159 = 1
Answer : The vectors u and v are parallel.