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Let the position vectors of points ‘A’ a...

Let the position vectors of points ‘A’ and ‘B’ be `hat(i)+hat(j) + hat(k)` and `2hat(i)+hat(j)+3hat(k)`, respectively. A point ‘P’ divides the line segment AB internally in the ratio `lambda:1(lambda gt 0)`. If O is the origin and `vec(OB).vec(OP)-3|vec(OA)xx vec(OP)|^(2)=6`, then `lambda` is equal to ________

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