Let a = ( 3 - 4 cos) i - ( 4 sin ) j , b = ( 4 - 5 sin ) i - ( 5 cos ) j , for ( 0 , 2 ) . Then the least value of | a | + | b | is

Question

$Let \bar{a} = (3 - 4 \cos θ) \hat{i} - (4 \sin θ) \hat{j}, \bar{b} = (4 - 5 \sin θ) \hat{i} - (5 \cos θ) \hat{j}, for θ \in (0, \frac{π}{2}) .$

$Then the least value of$ $| \bar{a} |$ $+$ $| \bar{b} |$ $is$

Smart Achievers · Accepted Answer

(3)

$\bar{D C} = \bar{a},$ $\bar{A B} = \bar{b},$ $\bar{O A} = q \hat{i}$

$Rotate ∆ O A B by 30 ° then A reaches C. B reaches B' where$ $| \bar{A B} |$ $=$ $| \bar{C B'} |$

$| \bar{D} C |$ $+$ $| \bar{C} B' |$ $is minimum if they are collinear$

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