Vectors 3 Question 6

6. The value of a, so that the volume of parallelopiped formed by i^+aj^+k^,j^+ak^ and ai^+k^ become minimum, is

(2003, 1M)

(a) -3

(b) 3

(c) 1/3

(d) 3

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Answer:

Correct Answer: 6. (c)

Solution:

  1. We know that, volume of parallelopiped whose edges are a,b,c=[abc].

[abc]=|1a1 01a a01|=1+a3a

Let f(a)=a3a+1

f(a)=3a21

f(a)=6a

For maximum or minimum, put f(a)=0

a=±13, which shows f(a) is minimum at a=13 and maximum at a=13.



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