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Question

Given than q2−pr<0,p>0 the value of ∣∣ ∣∣pqpx+qyqrqx+rypx+qyqx+ry0∣∣ ∣∣ is

A
zero
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B
positive
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C
negative
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D
q2+pr
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Solution

The correct option is C negative
∣ ∣pqpx+qyqrqx+rypx+qyqx+ry0∣ ∣
C3C3(xC1+yC2)
∣ ∣ ∣pq0qr0px+qyqx+ry(px2+2qxy+ry2)∣ ∣ ∣
=(px2+2qxy+ry2)(q2pr)
Substitute y=mx and then the expression becomes (p+2qm+rm2)(x2)(q2pr)
Everything in the above expression is +ve except (q2pr)

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