Scalar Product in a Plane

Given vectors u and v, what is the scalar product u·v?

• u·u = x^2 + y^2 +2xy

• ||u||·||v||·sinθ

• xx' + yy'

• ||u||·||v||·cosθ

What is the magnitude of vector u?

• ||u|| = √(u^2) = √(x^2 + y^2)

• ||u|| = x + y

• ||u|| = x - y

• ||u|| = x^2 + y^2

What does it mean if 0<k<1 in the context of vectors u=kv?

• u and v have the same sense

• u and v have opposite sense

• u is greater than v

• u is less than v

Which of the following is correct

• u·v = v·u

• u·(v+w)=u.v+u.w

• u·v =u x v

• u·v = 0 then u and v are parallel

What is the distributive property of scalar products?

• u·(v + w) = u·v + v·w

• u·(v + w) = u·v + u·w

• (u+v)·(w-z)=

  u·w-u·v+v·w-v·z

• u·(v + w) = w·(v + u)

What is the result of (u - v)^2?

• u^2 - 2·u·v + v^2

• u^2 + v^2

• u·v

• 0

Two vectors are collinear if _

• their ratio is a constant

• their dot product is zero

• xx'+yy'+cos(theta)=0

The dot product of 2 vectors represent _

• a new vector

• the sum of their components

• their alignment

• a real number

the cos of angle between these u=(2,1) and v=(1,2) is

• -0.8

• 0.8

• 0.64

• 36.87

if u=(1,1) and v=(-1,1), then

• u and v are parallel

• u=kv

• u and v are perpendicular

• theta = -pi