Let `hata and hatb` be two unit vectors. If the vectors `vecc=hata+2hatb and vecd=5hata-4hatb` are perpendicular to each other then the angle between `hata and hatb` is (A) `pi/2` (B) `pi/3` (C) `pi/4` (D) `pi/6`A. `(pi)/(6)`B. `(pi)/(2)`C. `(pi)/(3)`D. `(pi)/(4)`

Let `hata and hatb` be two unit vectors. If the vectors `vecc=hata+2ha

1.	Let `hata and hatb` be two unit vectors. If the vectors `vecc=hata+2hatb and vecd=5hata-4hatb` are perpendicular to each other then the angle between `hata and hatb` is (A) `pi/2` (B) `pi/3` (C) `pi/4` (D) `pi/6`A. `(pi)/(6)`B. `(pi)/(2)`C. `(pi)/(3)`D. `(pi)/(4)`
Answer» Correct Answer - C Given, c and d are perpendicular to each other, `therefore cd = 0` `rArr (hata + 2hatb)(5 hata - 4 hatb) = 0 ` `rArr 5 hata * hata - 4 hat a hat b + 10 hat b hata - 8 hatb * hatb = 0 ` ` rArr 6 hata * hatb = 3 ` `rArr hata *hatb = (1)/(2)` So, the angle between `hata and hatb` is `(pi)/(3)`.

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Let `hata and hatb` be two unit vectors. If the vectors `vecc=hata+2hatb and vecd=5hata-4hatb` are perpendicular to each other then the angle between `hata and hatb` is (A) `pi/2` (B) `pi/3` (C) `pi/4` (D) `pi/6`A. `(pi)/(6)`B. `(pi)/(2)`C. `(pi)/(3)`D. `(pi)/(4)`

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