Statement 1- If A-2-3-6k- B-2k- and C-2-k- then -A-A-A-B-C-243Statement 2- -A-A-A-B-C-A-2-ABC-

A×((A·B)A (A·A)B)·C ={A×(A·B)A (A·A)A×B}C = |A|^2[ABC] Now, |A|^2=4+9+36=49 [ABC]= 2 amp;3 amp;6 1 amp;1 amp; 2 1 amp;2 amp;1 =2(1+4) 1(3 12)+1( 6 ...

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Byju's Answer

Standard XII

Mathematics

Vector Triple Product

Statement 1: ...

Question

Statement $1$ : If $\to A = 2^i + 3^j + 6^k, \to B =^i +^j - 2^k$ and $\to C =^i + 2^j +^k$ , then $| \to A \times (\to A \times (\to A \times \to B)) \cdot \to C | = 243$

Statement $2$ : $| \to A \times (\to A \times (\to A \times \to B)) \cdot \to C | = | \to A |^{2} | [\to A \to B \to C] |$

Both the statements are true and statement

2

is the correct explanation for Statement

1

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Both the statements are true but Statement

2

is not the correct explanation for Statement

1

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Statement

1

is false and Statement

2

is true

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Statement

1

is false and Statement

2

is false

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Solution

The correct option is C Statement $1$ is false and Statement $2$ is true
$\to A \times ((\to A \cdot \to B) \to A - (\to A \cdot \to A) \to B) \cdot \to C$
$= {\to A \times (\to A \cdot \to B) \to A - (\to A \cdot \to A) \to A \times \to B} \to C$
$= - | \to A |^{2} [\to A \to B \to C]$
Now, $| \to A |^{2} = 4 + 9 + 36 = 49$
$[\to A \to B \to C] = ∣ ∣ ∣ ∣ \begin{matrix} 2 & 3 & 6 1 & 1 & - 2 1 & 2 & 1 \end{matrix} ∣ ∣ ∣ ∣$
$= 2 (1 + 4) - 1 (3 - 12) + 1 (- 6 - 6)$
$= 7$

$| - | \to A |^{2} [\to A \to B \to C] | = 49 \times 7 = 343$

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Similar questions

Q. Statement

1

: If

\to A = 2^i + 3^j + 6^k, \to B =^i +^j - 2^k

and

\to C =^i + 2^j +^k

, then

| \to A \times (\to A \times (\to A \times \to B)) \cdot \to C | = 243

Statement

2

| \to A \times (\to A \times (\to A \times \to B)) \cdot \to C | = | \to A |^{2} | [\to A \to B \to C] |

If \to a = 2^i + 3^j +^k, \to b =^i - 2^j +^k and \to c = - 3^i +^j + 2^k,

find

[\to a \to b \to c] .

Q. Find

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

,if

\to a = 2^i +^j + 3^k, \to b = -^i + 2^j +^k a n d \to c = 3^i +^j + 2^k

Find $\to a . (\to b \times \to c)$ , if $\to a = 2^i +^j + 3^k, \to b = -^i + 2^j +^k$ and $\to c = 3^i +^j + 2^k$ .

Q. If

\to r = 3^i + 2^j - 5^k, \to a = 2^i -^j +^k, \to b =^i + 3^j - 2^k

and

\to c = - 2^i +^j - 3^k

such that

\to r = x \to a + y \to b + z \to c

, then

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Statement 1: If →A=2^i+3^j+6^k, →B=^i+^j−2^k and →C=^i+2^j+^k, then |→A×(→A×(→A×→B))⋅→C|=243 Statement 2: |→A×(→A×(→A×→B))⋅→C|=|→A|2|[→A→B→C]|

Statement $1$ : If $\to A = 2^i + 3^j + 6^k, \to B =^i +^j - 2^k$ and $\to C =^i + 2^j +^k$ , then $| \to A \times (\to A \times (\to A \times \to B)) \cdot \to C | = 243$

Statement $2$ : $| \to A \times (\to A \times (\to A \times \to B)) \cdot \to C | = | \to A |^{2} | [\to A \to B \to C] |$