Let a-b-c- be vectors of length 3-4-5 respectively- Let a- be perpendicular to b-c-b- to c-a- and c- to a-b- Then a-b-c- is

The correct option is D 5√(2) a⃗+b⃗+c⃗=√((a⃗+b⃗+c⃗)^2) =√(a^2+b^2+c^2+2[ a⃗.b⃗+b⃗.c⃗+c⃗.a⃗ ]) Modulus formula for vectors ∵ a⃗.[ b⃗+c⃗ ]=0, b⃗.[ ...

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Byju's Answer

Standard XII

Mathematics

Addition of Vectors

Let a⃗,b⃗,c...

Question

Let $\to a, \to b, \to c$ be vectors of length $3, 4, 5$ respectively. Let $\to a$ be perpendicular to $\to b + \to c, \to b t o \to c + \to a$ and $\to c t o \to a + \to b$ . Then $∣ ∣ \begin{matrix} \to a + \to b + \to c \end{matrix} ∣ ∣$ is

2 \sqrt{5}

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2 \sqrt{2}

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10 \sqrt{5}

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5 \sqrt{2}

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Solution

The correct option is D $5 \sqrt{2}$
$∣ ∣ \begin{matrix} \to a + \to b + \to c \end{matrix} ∣ ∣ = \sqrt{(\to a + \to b + \to c)^{2}} = \sqrt{a^{2} + b^{2} + c^{2} + 2 (\begin{matrix} \to a . \to b + \to b . \to c + \to c . \to a \end{matrix})}$ {Modulus formula for vectors}
$∵ \to a . (\begin{matrix} \to b + \to c \end{matrix}) = 0, \to b . (\begin{matrix} \to c + \to a \end{matrix}) = 0 & \to c . (\begin{matrix} \to a + \to b \end{matrix}) = 0$ [As the given conditions of being perpendicular}
$\Rightarrow \to a . \to b + \to b . \to c + \to c . \to a = 0$ {expanding the previous expression and substituting in the first expression}
$\Rightarrow ∣ ∣ \begin{matrix} \to a + \to b + \to c \end{matrix} ∣ ∣ = \sqrt{a^{2} + b^{2} + c^{2}} = \sqrt{3^{2} + 4^{2} + 5^{2}} = 5 \sqrt{2}$

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Similar questions

Q. Let

\to a, \to b, \to c

be vectors of length

3, 4, 5

respectively. Let

\to a

be perpendicular to

\to b + \to c, \to b

\to c + \to a

\to c

\to a + \to b .

Then

∣ ∣ \to a + \to b + \to c ∣ ∣

is:

Q. Let

\to a, \to b, \to c

be three units vectors such that

\to a \times (\to b \times \to c) = \frac{\to b + \to c}{\sqrt{2}}

and the angles between

\to a, \to c

and

\to a, \to b

α

and

β

respectively, then

Q. Let

\to a, \to b, \to c

be vectors of length

3, 4

and

5

respectively. Let

\to a

be perpendicular to

(\to b + \to c), \to b

(\to c + \to a)

and

\to c

(\to a + \to b)

. Find the length of the vector

\to a + \to b + \to c

Q. Let

\to A = \to b \times \to c, \to B = \to c \times \to a, \to C = \to a \times \to b

, then the vectors

\to A \times (\to B \times \to C)

\to B \times (\to C \times \to A)

, and

\to C \times (\to A \times \to B)

are

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} .

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is perpendicular to vector

\to b \times \to c

, then

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

is equal to

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Let →a,→b,→c be vectors of length 3,4,5 respectively. Let →a be perpendicular to →b+→c,→bto→c+→a and →cto→a+→b. Then ∣∣→a+→b+→c∣∣ is

Let $\to a, \to b, \to c$ be vectors of length $3, 4, 5$ respectively. Let $\to a$ be perpendicular to $\to b + \to c, \to b t o \to c + \to a$ and $\to c t o \to a + \to b$ . Then $∣ ∣ \begin{matrix} \to a + \to b + \to c \end{matrix} ∣ ∣$ is