Question

find the product of PQ, PQR ,R

Answer 1

PQ × PQR × R
P2 Q2 R 2

2 =SQUARE

Answer 2

Hey there,

Answer:

ˆPQR=cos−1(27√1235)

Explanation:

Be two vectors −−→AB and −−→AC :

−−→AB⋅−−→AC=(AB)(AC)cos(ˆBAC)
=(xABxAC)+(yAByAC)+(zABzAC)

We have:

P=(1;1;1)
Q=(−2;2;4)
R=(3;−4;2)

therefore

−−→QP=(xP−xQ;yP−yQ;zP−zQ)=(3;−1;−3)
−−→QR=(xR−xQ;yR−yQ;zR−zQ)=(5;−6;−2)

and

(QP)=√(xQP)2+(yQP)2+(zQP)2=√9+1+9=√19

(QR)=√(xQR)2+(yQR)2+(zQR)2=√25+36+4=√65

Therefore:

−−→QP⋅−−→QR=√19√65cos(ˆPQR)
=(3⋅5+(−1)(−6)+(−3)(−2))

→cos(ˆPQR)=15+6+6√19√65=27√1235

→ˆPQR=cos−1(27√1235)