Let a- - - - - k- c- - - k- and a vector b be such that a-b-c and a -b-3- Then -b- equals -

We have a× nbsp;b=c a×(a× nbsp;b)= nbsp; nbsp;a×c (a. nbsp;b)a (a .a )b= a×c 3a 3b= 2î + nbsp;ĵ + nbsp;k̂ 3î + 3ĵ + 3k̂ 3b= 2î + nbsp;ĵ + ...

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Byju's Answer

Standard XII

Physics

Work Done as Dot Product

Let a= î + ĵ ...

Question

$Let \to a =^i +^j +^k, \to c =^j -^k$ and a vector $\to b$ be such that $\to a \times \to b = \to c$ and $\to a . \to b = 3$ . Then $| \to b |$ equals :

\frac{11}{3}

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\frac{11}{\sqrt{3}}

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\sqrt{\frac{11}{3}}

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\frac{\sqrt{1} 1}{3}

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Solution

The correct option is C $\sqrt{\frac{11}{3}}$
We have
$\to a \times \to b = \to c \to a \times (\to a \times \to b) = \to a \times \to c (\to a . \to b) \to a - (\to a . \to a) \to b = \to a \times \to c 3 \to a - 3 \to b = - 2^i +^j +^k 3^i + 3^j + 3^k - 3 \to b = - 2^i +^j +^k \to b = \frac{1}{3} (5^i + 2^j + 2^k) | \to b | = \sqrt{\frac{11}{3}}$

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Similar questions

Q. Let

\to a =^i +^j +^k, \to c =^j -^k

and a vector

\to b

be such that

\to a \times \to b = \to c

and

\to a \cdot \to b = 3

. Then

| \to b |

equals?

Q. Let

\to a =^i -^j, \to b =^i +^j +^k

and

\to c

be a vector such that

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

and

\to a \cdot \to c = 4

, then

| \to c |^{2}

is equal to:

Q. Let

\to a =^i +^j +^k

and

\to b =^j -^k .

\to c

is a vector such that

\to a \times \to c = \to b

and

\to a \cdot \to c = 3,

then

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

is equal to

Q. Given that

\to a =^i +^j +^k, \to c =^j -^k

and

\to a . \to b = 3, \to a \times \to b = \to c

then

3 \to b =

Q. Let

\to a =^i - 2^j +^k

and

\to b =^i -^j +^k

be two vectors. If

\to c

is a vector such that

\to b \times \to c = \to b \times \to a

and

\to c \cdot \to a = 0

, then

\to c \cdot \to b

is equal to :

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Let →a=^i+^j+^k,→c=^j−^k and a vector →b be such that →a×→b=→c and →a.→b=3. Then |→b| equals :

The correct option is C √113 We have →a×→b=→c→a×(→a×→b)=→a×→c(→a.→b)→a−(→a.→a)→b=→a×→c3→a−3→b=−2^i+^j+^k3^i+3^j+3^k−3→b=−2^i+^j+^k→b=13(5^i+2^j+2^k)|→b|=√113

$Let \to a =^i +^j +^k, \to c =^j -^k$ and a vector $\to b$ be such that $\to a \times \to b = \to c$ and $\to a . \to b = 3$ . Then $| \to b |$ equals :