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+1 vote
2.4k views
in Vector algebra by (36.3k points)

Let PR = 3i + j – 2k and SQ = i – 3j – 4k determine diagonals of a parallelogram PQRS and PT = i + 2j + 3k be another vector. The volume of the parallelopiped determined by the vectors PT, PQ and PS is

(a) 5 

(b) 20 

(c) 10 

(d) 30

1 Answer

+1 vote
by (33.0k points)
selected by
 
Best answer

Answer is (b) 20

Explanation:

When diagonal are given, then area of a parallelogram PQRS = (1/2) |PQ × SQ|

Volume of the parallelopiped

= ((PQ × PS)).PT

= |3(– 9 + 8) – (3 + 4) – 2(2 + 3)|

= | – 3 – 7 – 10|

= 20

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