If A(3, -2, 2) and B(2, lambda+1, 5) are the | vedclass

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(B) The angle subtended by the diameter at any point on the circle is a right angle. Therefore,$\angle APB = 90^{\circ}$,which implies $AP \perp PB$.T

Vedclass · Accepted Answer

$8$

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(B) The angle subtended by the diameter at any point on the circle is a right angle. Therefore,$\angle APB = 90^{\circ}$,which implies $AP \perp PB$.The direction ratios of $AP$ are $(5-3, 6-(-2), -1-2) = (2, 8, -3)$.The direction ratios of $PB$ are $(2-5, \lambda+1-6, 5-(-1)) = (-3, \lambda-5, 6)$.Since $AP \perp PB$,the dot product of their direction ratios must be zero:$(2)(-3) + (8)(\lambda-5) + (-3)(6) = 0$$-6 + 8\lambda - 40 - 18 = 0$$8\lambda - 64 = 0$$8\lambda = 64$$\lambda = 8$.

If $A(3, -2, 2)$ and $B(2, \lambda+1, 5)$ are the end points of the diameter of a circle and the point $P(5, 6, -1)$ lies on the circle,then $\lambda=$

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