Question

1. If p = 3,4 =-5, and r = 4, find the value of :
(ii) q² – 3pr
(v) 3pq + 10pr + 2qr
(1) p² - 2qr
(i) pg + qr + rp
(iii) r2 - pq
(vi) p² + q2 + r2 - Pq - qr - pr
8. If a = 3, and b = -4, find the value of:​

Answer 1

Answer:

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Let P(3,4,5) Q(4,6,3) R(−1,2,4) and S(1,0,5) be any four points.

The dr's of the line PQ are (1,2,−2)

The dr's of the line RS are (2,−2,1)

The projection of RS on PQ will be RS×cosθ

RScosθ =

∣PQ∣

PQ×RS

=

3

(i+2j−2k).(2i−2j+k)

=

3

4