If a is a vector of magnitude 50 , collinear with the vector b = 6 i ^ − 8 j ^ − 2 15 k ^ and makes an acute angle with the positive direction of Z - axis, then a is equal to

Question

If a is a vector of magnitude 50 , collinear with the vector b = 6 i ^ − 8 j ^ ​ − 2 15 ​ k ^ and makes an acute angle with the positive direction of Z - axis, then a is equal to

TestHub · Accepted Answer

Since a = m b for some scalar m i.e., a = m ( 6 i ^ − 8 j ^ ​ − 2 15 ​ k ^ ) ⇒ ∣ a ∣ = ∣ m ∣ 36 + 64 + 4 225 ​ ​ ⇒ 50 = 2 25 ​ ∣ m ∣ ⇒ ∣ m ∣ = 4 ⇒ m = ± 4 ​ Since, a makes an acute angle with the positive direction of Z - axis, so its z component must be positive and hence, m must be − 4 . ∴ a = − 4 ( 6 i ^ + 8 j ^ ​ − 2 15 ​ k ^ ) = − 24 i ^ + 32 j ^ ​ + 30 k ^

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