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Which of th efollowing is/are correct regarding vectors `vec(A) = 2hat(i) + hat(j)` and `vec(B) = 2hat(i) - 4 hat(j)`.A. Angle between `vec(A)` and `vec(B)` is acuteB. Angle between `vec(A) + vec(B)` and `vec(A)` is acuteC. `hat(k)` is a unit vector perpendicular to `vec(A)`D. `(hat(i) - 2 hat(j))/(sqrt5)` is a unit vector perpendicular to `vec(A)` |
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Answer» Correct Answer - B::C::D (A) `vec(A).vec(B) = AB cos theta = 0` `rArr theta = 90^(@)` Angle between `vec(A)` & `vec(B)` in `90^(@)` (B) `vec(A) + vec(B) = 4 hat(i) - 3 hat(j)` `(vec(A) + vec(B)).vec(A) = 8 - 3` `= 5 (+ve)` So, angle between `vec(A) + vec(B)` & `vec(A)` in acute (C ) z-axis is perpendicular to `x - y` plae `|(hat(i) - 2 hat(j))/(sqrt5)| = 1` `(2 hat(i) + hat(j)).((hat(i) - 2 hat(j))/(sqrt5)) = 0` |
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