Vectors: Angles, Projections, Parallel, Orthogonal, etc

Find the angle between vectors <1,3> and <2,-5>. Round to the nearest hundredth.

How do you know if two vectors are parallel?

• When the sum of the two vectors is 0.

• When one vector is a scalar multiple of the other.

• The angle between them is 90°.

• The dot product is 0.

Find the angle between the two vectors: Round to the nearest tenth.

Find the angle between the two vectors <3, 4> and <4, -3>

Find the angle between v and w. Round to the nearest tenth.

Find the projection of vector u onto vector v when given;

u =〈3,2〉and  v =〈5,-5〉 

If the dot product of two vectors is equal to zero, then what do we know about the two vectors?

• They are parallel.

• They are orthogonal.

• They are neither parallel nor orthogonal.

If vector u= <4,-2> and vector v= <6,8>; find the component of vector u along vector v.

Find the projection of vector u onto vector v when given:   $u\ =\ <-6,\ -6>$  and  $v\ =\ <-9,\ -3>$  

•  $<-7.2,\ -2.4>$  

•  $<3,\ 1>$  

•  $<-6.1,\ -2.3>$  

•  $<-9,\ -3>$  

Determine if the vectors are parallel, orthogonal, or neither. $<4,\ -2>$  and  $<6,\ 12>$  

• Parallel

• Orthogonal

• Neither