If a-b-c-0 and -a-3-b-4 and -c-37- the angle between a and b isA-B- 4C-D- 1-6

The correct option is A π/3a+b+c=0 ⇒ a+b= c ⇒ |a+b|^2=|c|^2 ⇒ |a|^2+|b|^2+2a.b=|c|^2 ⇒ 9+16+2(3)(4)cos (a,b)=37 ⇒ 24 cos (a,b)=12 ⇒ cos (a,b)=1/2⇒ (a,b)=π/3 ...

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Byju's Answer

Standard XII

Mathematics

Applications of Dot Product

If a+b+c=0 an...

Question

If a+b+c=0 and |a|=3, |b|=4 and $| c | = \sqrt{37}$ , the angle between a and b is

\frac{π}{4}

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\frac{π}{2}

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\frac{π}{6}

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\frac{π}{3}

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Solution

The correct option is D $\frac{π}{3}$
$a + b + c = 0 \Rightarrow a + b = - c \Rightarrow | a + b |^{2} = | c |^{2} \Rightarrow | a |^{2} + | b |^{2} + 2 a . b = | c |^{2} \Rightarrow 9 + 16 + 2 (3) (4) c o s (a, b) = 37 \Rightarrow 24 c o s (a, b) = 12 \Rightarrow c o s (a, b) = \frac{1}{2} \Rightarrow (a, b) = \frac{π}{3}$

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If a+b+c=0 and |a|=3, |b|=4 and |c|=√37, the angle between a and b is

The correct option is D π3a+b+c=0⇒a+b=−c⇒|a+b|2=|c|2⇒|a|2+|b|2+2a.b=|c|2⇒9+16+2(3)(4)cos(a,b)=37⇒24cos(a,b)=12⇒cos(a,b)=12⇒(a,b)=π3

If a+b+c=0 and |a|=3, |b|=4 and $| c | = \sqrt{37}$ , the angle between a and b is