The position vector of a point P is r = x i + y j + z k where x and y are positive integers and a = i + j + k . If r ⋅ a = 10 , then the number of possible positions of P is :

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MathematicsPermutation & CombinationDivision of Identical itemsEasy2 minQB

MathematicsEasysingle choice

The position vector of a point P is $r = x i + y j + z k$ where x and y are positive integers and $a = i + j + k$ . If $r \cdot a = 10$ , then the number of possible positions of P is :

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Answer:

Solution:

$r . a = x + y + z$

$∴ x + y + z = 10$ where x and y are positive integers.

∴ No. of positive integral solutions of

$X + y + z = 10$ is $(10 - 1) C_{3 - 1} = 9 C_{2} = 36$ .

Stream:JEESubject:MathematicsTopic:Permutation & CombinationSubtopic:Division of Identical items

⏱ 2mℹ️ Source: QB

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