If a-b- c- be three vectors such that -a-b-c-1- c-a-b- and -a-1-2- -b-1-3- -c-1-6- then the angle between a- and b- is

The correct option is C #10; π2 #10; √((a⃗+b⃗)^2+c⃗^2)=1 a⃗^2+b^2+2a⃗.b⃗+c^2=1 12+13+2a⃗.b⃗+16=1 2a⃗.b⃗=o a⃗.b⃗=o So a⃗ ...

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Byju's Answer

Standard XII

Mathematics

Applications of Dot Product

If a⃗,b⃗, c...

Question

If $\to a, \to b, \to c$ be three vectors such that $| \to a + \to b + \to c | = 1, \to c = λ (\to a \times \to b)$ and $| \to a | = \frac{1}{\sqrt{2}}, | \to b | = \frac{1}{\sqrt{3}}, | \to c | = \frac{1}{\sqrt{6}}$ , then the angle between $\to a$ and $\to b$ is

\frac{π}{6}

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\frac{π}{4}

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\frac{π}{3}

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\frac{π}{2}

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Solution

The correct option is C $\frac{π}{2}$
$\sqrt{(\to a + \to b)^{2} + {\to c}^{2}} = 1$
${\to a}^{2} + b^{2} + 2 \to a . \to b + c^{2} = 1$
$\frac{1}{2} + \frac{1}{3} + 2 \to a . \to b + \frac{1}{6} = 1$
$2 \to a . \to b = o$
$\to a . \to b = o$
So $\to a$ & $\to b$ are $⊥$ to each other

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Similar questions

Q. 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 |

Q. Let

\to a, \to b, \to c

be three non-zero vectors such that

\to c

is a unit vectors perpendicular is both

\to a

and

\to b

. If the angle between

\to a

and

\to b

\frac{π}{6}

, prove that

[\to a \to b \to c]^{2} = \frac{1}{4} | \to a |^{2} | \to b |^{2}

Q. If

\to a, \to b, \to c

are unit vectors such that

\to a + \to b + \to c = \to 0

and

(\to a, \to b) = \frac{π}{3}

, then

∣ ∣ \to a \times \to b ∣ ∣ + ∣ ∣ \to b \times \to c ∣ ∣ + | \to c \times \to a | =

Q. Let

\to a, \to b

and

\to c

be three vectors such that

| \to a | = \sqrt{3}, | \to b | = 5, \to b . \to c = 10

and the angle between

\to b

and

\to c

\frac{π}{3} .

\to a

is perpendicular to vector

\to b \times \to c

, then

| \to a \times (\to b \times \to c) |

is equal to

Q. Let

\to A, \to B

and

\to C

be unit vectors. Suppose that

\to A \cdot \to B = \to A \cdot \to C = 0

and that the angle between

\to B

and

\to C

\frac{π}{6}

then

\to A =

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If →a,→b, →c be three vectors such that |→a+→b+→c|=1, →c=λ(→a×→b) and |→a|=1√2, |→b|=1√3, |→c|=1√6, then the angle between →a and →b is

The correct option is C π2 √(→a+→b)2+→c2=1→a2+b2+2→a.→b+c2=112+13+2→a.→b+16=12→a.→b=o→a.→b=oSo →a & →b are ⊥ to each other

If $\to a, \to b, \to c$ be three vectors such that $| \to a + \to b + \to c | = 1, \to c = λ (\to a \times \to b)$ and $| \to a | = \frac{1}{\sqrt{2}}, | \to b | = \frac{1}{\sqrt{3}}, | \to c | = \frac{1}{\sqrt{6}}$ , then the angle between $\to a$ and $\to b$ is

The correct option is C $\frac{π}{2}$
$\sqrt{(\to a + \to b)^{2} + {\to c}^{2}} = 1$
${\to a}^{2} + b^{2} + 2 \to a . \to b + c^{2} = 1$
$\frac{1}{2} + \frac{1}{3} + 2 \to a . \to b + \frac{1}{6} = 1$
$2 \to a . \to b = o$
$\to a . \to b = o$
So $\to a$ & $\to b$ are $⊥$ to each other