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∣∣
∣∣ C3→C3−(xC1+yC2) ∣∣
∣
∣∣pq0qr0px+qyqx+ry−(px2+2qxy+ry2)∣∣
∣
∣∣ =(px2+2qxy+ry2)(q2−pr) Substitute y=mx and then the expression becomes (p+2qm+rm2)(x2)(q2−pr) Everything in the above expression is +ve except (q2−pr)