If a- and b- are two unit vectors such that a- - 2 b- and 5 a- - 4 b- are perpendicular to each other- then the angle between a- and b- is

Since, ( a⃗ +2 b⃗ ). ( 5 a⃗ 4 a⃗ ) = 0 ⇒ 5|a⃗|^2 + 6a⃗. b⃗ 8|b⃗|^2 = 0 ⇒ 6 a⃗. b⃗ = 3 [∵ |a⃗|= |b⃗|=1] ⇒cos θ = 1/2⇒θ = 60^∘ ...

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Byju's Answer

Standard XIII

Mathematics

Angle between Two Vectors

If a⃗ and b⃗ ...

Question

If $\to a$ and $\to b$ are two unit vectors such that $\to a + 2 \to b$ and $5 \to a - 4 \to b,$ are perpendicular to each other, then the angle between $\to a$ and $\to b$ is

45^{\circ}

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60^{\circ}

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c o s^{- 1} (\frac{1}{3})

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c o s^{- 1} (\frac{2}{7})

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Solution

The correct option is B $60^{\circ}$
Since, $(\to a + 2 \to b) . (5 \to a - 4 \to a) = 0 \Rightarrow 5 | \to a |^{2} + 6 \to a . \to b - 8 | \to b |^{2} = 0 \Rightarrow 6 \to a . \to b = 3 [∵ | \to a | = | \to b | = 1] \Rightarrow cos θ = \frac{1}{2} \Rightarrow θ = 60^{\circ}$

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If →a and →b are two unit vectors such that →a+2→b and 5 →a−4 →b, are perpendicular to each other, then the angle between →a and →b is

The correct option is B 60∘Since, (→a+2→b).(5→a−4→a)=0⇒5|→a|2+6→a.→b−8|→b|2=0⇒6→a.→b=3[∵|→a|=|→b|=1]⇒cos θ =12⇒θ=60∘

If $\to a$ and $\to b$ are two unit vectors such that $\to a + 2 \to b$ and $5 \to a - 4 \to b,$ are perpendicular to each other, then the angle between $\to a$ and $\to b$ is

The correct option is B $60^{\circ}$
Since, $(\to a + 2 \to b) . (5 \to a - 4 \to a) = 0 \Rightarrow 5 | \to a |^{2} + 6 \to a . \to b - 8 | \to b |^{2} = 0 \Rightarrow 6 \to a . \to b = 3 [∵ | \to a | = | \to b | = 1] \Rightarrow cos θ = \frac{1}{2} \Rightarrow θ = 60^{\circ}$