If a-b-c- are unit vectors and the angles between a-b- and b-c- and c-a- are -6-3 and -4 respectively- then -a-b-c-

The correct option is D None of these |a⃗+b⃗+c⃗| =√(a⃗.a⃗+b⃗.b⃗+c⃗.c⃗+2(a⃗.b⃗+b⃗.c⃗+c⃗.a⃗)) =√(a^2+b^2+c^2+2(abcosθ+bccosγ+accosβ)) =√(3+2(c ...

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Byju's Answer

Standard XII

Mathematics

Applications of Dot Product

If a⃗,b⃗,c⃗...

Question

If $\to a, \to b, \to c$ are unit vectors and the angles between $\to a, \to b$ and $\to b, \to c$ and $\to c, \to a$ are $\frac{π}{6}, \frac{π}{3}$ and $\frac{π}{4}$ respectively, then $| \to a + \to b + \to c |$

3

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4 + \sqrt{3} + \sqrt{2}

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\sqrt{4 + 3 + 2}

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None of these

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Solution

The correct option is D None of these
$| \to a + \to b + \to c |$

$= \sqrt{\to a . \to a + \to b . \to b + \to c . \to c + 2 (\to a . \to b + \to b . \to c + \to c . \to a)}$

$= \sqrt{a^{2} + b^{2} + c^{2} + 2 (a b cos θ + b c cos γ + a c cos β)}$

$= \sqrt{3 + 2 (cos 60^{0} + cos 30^{0} + cos 45^{0})}$

$= \sqrt{3 + 2 (\frac{1}{2} + \frac{\sqrt{3}}{2} + \frac{1}{\sqrt{2}})}$

$= \sqrt{4 + \sqrt{3} + \sqrt{2}}$

Suggest Corrections

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If →a,→b,→c are unit vectors and the angles between →a,→b and →b,→c and →c,→a are π6,π3 and π4 respectively, then |→a+→b+→c|

The correct option is D None of these|→a+→b+→c|=√→a.→a+→b.→b+→c.→c+2(→a.→b+→b.→c+→c.→a)=√a2+b2+c2+2(abcosθ+bccosγ+accosβ)=√3+2(cos600+cos300+cos450)=√3+2(12+√32+1√2)=√4+√3+√2

If $\to a, \to b, \to c$ are unit vectors and the angles between $\to a, \to b$ and $\to b, \to c$ and $\to c, \to a$ are $\frac{π}{6}, \frac{π}{3}$ and $\frac{π}{4}$ respectively, then $| \to a + \to b + \to c |$