If a → = x i ^ + y j ^ + z k ^ , b → = ı ^ + j ^ + k ^ where x , y , z ∈ 0,3 , - 3,6 , - 6 , then the number of non-zero vectors a → such that a → · b → = 0 are

Question

If a → = x i ^ + y j ^ + z k ^ , b → = ı ^ + j ^ + k ^ where x , y , z ∈ 0,3 , - 3,6 , - 6 , then the number of non-zero vectors a → such that a → · b → = 0 are, 20, 18, 15, 12

MARKS App · Accepted Answer

a → · b → = x + y + z = 0 If x = 3 , y = - 3 , z = 0 , i.e. 3 ! = 6 If x = 6 , y = - 6 , z = 0 , i.e. 3 ! = 6 If x = 6 , y = - 3 , z = - 3 , i.e. 3 ! 2 ! = 3 If x = - 6 , y = 3 , z = 3 , i.e. = 3 ! 2 ! = 3 Total number of vectors = 18

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