Question

the position vectors of P, Q and R are i+5j+k, -i-2j-2k and -j-k respectively. find ∠PQR.

How should i start ?

Answer 1

PQ = Q-P
QR = R-Q

|PQ||QP|cos(theta) = PQ.dot.QP

Answer 2

Find Vector P-Q
And Vector R-Q
Find the angle by using
\[(P-Q).(R-Q)=|P-Q||R-Q| \cos \theta\]
Find theta using above. Can you do it?

Answer 3

let me try, thanks

Answer 4

Is it PQ．RQ or QP．QR? and why?

Answer 5

P, Q and R are position vectors of point P, Q and R. If we want a vector directed from Q to P then it's P-Q or PQ.
and a vector directed from Q to R then it's R-Q or RQ
either choose PQ and RQ to find angle or choose QP and QR to find the angle

Answer 6

1)Find vector PQ and QR
2) Use vector Dot " . " product for angle,

> > PQ= -2i -7j-3k and QR= i+j+k

> now
PQ . QR = |PQ| |QR| Cos (theta)
=> 12 = (62)^1/2 (3)^1/2 Cos (theta)

Answer 7

why is that when a vector is directed from Q to P, it is PQ but a vector directed from Q to R, it is RQ

Answer 8

technically its not 'PQ',
thing IS we'r lazy, and wont spend a sec on something that basic

Answer 9

Sorry, but how do I mention a person in post ? ? ?
my browser seems unresponsive . . .

Answer 10

i understand that QR is from Q to R (alright i can't type the arrow signs here, just assume there are arrows) but why isn't PQ from P to Q?

to mention a person in post just type @ followed by the name of that person

Answer 11

@Callisto
PQ is indeed directed from P to Q, similarly a vec. from Q to P would be QP