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Mathematics - Vector Question with Solution | TestHub

MathematicsVectorAngle Between LinesMedium2 minQB

MathematicsMediumnumerical

If lines $bx = 1 - cy, bz = 1& bx = 2 + ay, bz = 3 + cy$ are perpendicular, where a,b,c are sides of $Δ ABC$ , then minimum value of $cos B$ is -

Answer:

0.50

Solution:

The direction ratios of the two lines are $(c, - b, 0)$ and $(a, b, c)$ . Perpendicularity gives $a c - b^{2} = 0$ , so $b^{2} = a c$ . Hence $cos B = \frac{a ^{2} + c ^{2} - b ^{2}}{2 a c} = \frac{1}{2} (\frac{a}{c} + \frac{c}{a}) - \frac{1}{2} \geq \frac{1}{2}$ , with equality at $a = c$ .

Stream:JEESubject:MathematicsTopic:VectorSubtopic:Angle Between Lines

⏱ 2mℹ️ Source: QB

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