If a → = i ^ + j ^ − 2 k ^ , b → = 2 i ^ − j ^ + k ^ and c → = 3 i ^ − k ^ . If c → = m a → + n b → then m + n =

Question

If a → = i ^ + j ^ − 2 k ^ , b → = 2 i ^ − j ^ + k ^ and c → = 3 i ^ − k ^ . If c → = m a → + n b → then m + n =, 0, 1, 2, − 1

MARKS App · Accepted Answer

c ¯ = m a ¯ + n b ¯ ⇒ 3 i ¯ - k ¯ = m i ¯ + m j ¯ - 2 m k ¯ + 2 n i ¯ - n j ¯ + n k ¯ ⇒ 3 i ¯ - k ¯ = m + 2 n i ¯ + m - n i ¯ + n - 2 m k ¯ ∴ m + 2 n = 3 ...... (i) m - n = 0 ...... (ii) n - 2 m = - 1 .... (iii) As m - n = 0 from (ii) ∴ m = n ∴ 3 m = 3 ∴ m = 1 a n d n = 1 ∴ m + n = 2

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