6-3 Orthogonal, Parallel and Projection Vector

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

•  $<-7.2,\ -2.4>$  

•  $<3,\ 1>$  

•  $<-6.1,\ -2.3>$  

•  $<-9,\ -3>$  

Find the projection vector of u onto v.    $u=<-9,\ -5>$   and   $v\ =\ <7,\ 1>$  

• $<7,\ 1>$

• $<3.5,\ 0.5>$

• $<-9.5,\ -1.4>$

• $<-1,\ 7>$

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

• Parallel

• Orthogonal

• Neither

• Both

Determine if the vectors are parallel, orthogonal, or neither.
 $<4,\ -6>$  and  $<-8,\ 12>$   

• Parallel

• Orthogonal

• Neither

• Both

Find the projection vector of u onto w.     $u\ =\ <-1,\ 3>$    and  $w\ =\ <2,\ -5>$  

•  $<-1.7,\ -5.1>$  

•  $<-5.1,\ -1.7>$  

•  $<-1.2,\ 2.9>$  

•  $<2.3,\ -4.9>$  

Determine if the vectors are parallel, orthogonal, or neither.
 $u\ =\ <4,\ -8>$  and  $<0,\ -9>$  

• Parallel

• Orthogonal

• Neither

• Both

Determine if the vectors are parallel, orthogonal, or neither.     $u\ =\ 4i\ -\ j$  and  $v\ =\ -3i\ -\ 12j$  

• Parallel

• Orthogonal 

• Neither

• Both

Determine if the vectors are parallel, orthogonal, or neither.     $u\ =\ -2i\ -9j$  and  $v\ =\ -6i\ -\ 27j$  

• Parallel

• Orthogonal 

• Neither

• Both

Find the projection of vector u onto w and then write vector u as the sum of two orthogonal vectors.     $u\ =\ <1,\ 3>$    and  $w\ =\ <2,\ 4>$  

•  $u\ =<1,\ 1>+<0,\ 2>$  

•  $u\ =\ <\frac{7}{5},\ \frac{14}{5}>+<-\frac{2}{5},\ \frac{1}{5}>$  

•  $u\ =\ <-\frac{189}{50},\ -\frac{27}{50}>+\ <\frac{239}{50},\ \frac{177}{50}>$  

•  $u\ =\ <-\frac{352}{65},\ -\frac{44}{65}>+<\frac{417}{65},\ \frac{239}{65}>$  

Find the projection of vector u onto v and then write vector u as the sum of two orthogonal vectors.       $u\ =\ <8,\ 6>$    and  $v\ =\ <4,\ 4>$  

•  $u\ =\ <1,\ -1>+<7,\ 7>$  

•  $u\ =<\frac{60}{13},\ \frac{40}{13}>+<\frac{34}{13},\ \frac{51}{13}>$  

•  $u\ =\ <\frac{63}{74},\ -\frac{45}{74}>+<-\frac{285}{74},\frac{399}{74}>$  

•  $u\ =\ <\frac{216}{89},\ \frac{135}{89}>+<\frac{140}{89},\ -\frac{224}{89}>$