The position vector of the point P is π → = x i ^ + y j ^ + z k ^ , where x , y , z ∈ N. If a → = i ^ + j ^ + k ^ and π → . a → = 10 , then the number of possible positions of point P is equal to

Question

The position vector of the point P is π → = x i ^ + y j ^ + z k ^ , where x , y , z ∈ N. If a → = i ^ + j ^ + k ^ and π → . a → = 10 , then the number of possible positions of point P is equal to, 36, 72, 66, 54

MARKS App · Accepted Answer

π → . a → = 10 ⇒ x + y + z = 10 The required number of positions = The number of positive integral solutions of x + y + z = 10 = C 3 - 1 10 - 1 = 9 × 8 2 = 36

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