If a¯, b¯ are unit vectors satisfying 5a¯+3b¯×3a¯-7b¯=0¯, thena¯, b¯ is

|a|=|b|=1 (5a+3b)×(3a-7b)=0 ⇒ 0-35 a×b+9 b×a-0=0 ⇒ -44(a×b)=0 ⇒ a×b=0 ⇒ a || b ⇒ a, b=0 or π

If a¯, b¯ are unit vectors satisfying 5a¯+3b¯×3a¯-7b¯=0¯, thena¯, b¯ is

|a|=|b|=1 (5a+3b)×(3a-7b)=0 ⇒ 0-35 a×b+9 b×a-0=0 ⇒ -44(a×b)=0 ⇒ a×b=0 ⇒ a || b ⇒ a, b=0 or π

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$If \bar{a}, \bar{b} are unit vectors satisfying (5 \bar{a} + 3 \bar{b}) \times (3 \bar{a} - 7 \bar{b}) = \bar{0}, then (\bar{a}, \bar{b}) is$

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$\frac{π}{2}$

$\frac{π}{3}$

$\frac{π}{6}$

$0 or π$

answer is D.

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Detailed Solution

$| a | = | b | = 1 (5 a + 3 b) \times (3 a - 7 b) = 0 \Rightarrow 0 - 35 a \times b + 9 b \times a - 0 = 0 \Rightarrow - 44 (a \times b) = 0 \Rightarrow a \times b = 0 \Rightarrow a | | b \Rightarrow a, b = 0 or π$

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If a¯, b¯ are unit vectors satisfying 5a¯+3b¯×3a¯-7b¯=0¯, thena¯, b¯ is

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$If \bar{a}, \bar{b} are unit vectors satisfying (5 \bar{a} + 3 \bar{b}) \times (3 \bar{a} - 7 \bar{b}) = \bar{0}, then (\bar{a}, \bar{b}) is$