If a→=3i^+2j^+3k^ , b→=4i^−3j^ , c→=i^+3j^ and d→=4j^−k^ then , List-I List-III)a→.b→=P)4i^−3j^II)a→×b→=Q)12III)c→×d→=R)9i^+12j^−17k^IV)c→.d→=S)−3i^+j^+4k^ T)6Which of the following option is correct

a¯.b¯=(3i+2j+3k)(4i−3j)=12−6=6 a¯×b¯=|ijk3234−30|=i(0+9)−j(0−12)+k(−9−8) a¯×b¯=9i+12j−17k c¯.d¯=12c¯×d¯=−3i^+j^+4k^

If a→=3i^+2j^+3k^ , b→=4i^−3j^ , c→=i^+3j^ and d→=4j^−k^ then , List-I List-III)a→.b→=P)4i^−3j^II)a→×b→=Q)12III)c→×d→=R)9i^+12j^−17k^IV)c→.d→=S)−3i^+j^+4k^ T)6Which of the following option is correct

a¯.b¯=(3i+2j+3k)(4i−3j)=12−6=6 a¯×b¯=|ijk3234−30|=i(0+9)−j(0−12)+k(−9−8) a¯×b¯=9i+12j−17k c¯.d¯=12c¯×d¯=−3i^+j^+4k^

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If $\vec{a} = 3 \hat{i} + 2 \hat{j} + 3 \hat{k}$ , $\vec{b} = 4 \hat{i} - 3 \hat{j}$ , $\vec{c} = \hat{i} + 3 \hat{j}$ and $\vec{d} = 4 \hat{j} - \hat{k}$ then ,
List-I List-II
I) $\vec{a} . \vec{b} =$ P) $4 \hat{i} - 3 \hat{j}$
II) $\vec{a} \times \vec{b} =$ Q) 12
III) $\vec{c} \times \vec{d} =$ R) $9 \hat{i} + 12 \hat{j} - 17 \hat{k}$
IV) $\vec{c} . \vec{d} =$ S) $- 3 \hat{i} + \hat{j} + 4 \hat{k}$
T) 6
Which of the following option is correct

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$I \to T, I I \to Q, I I I \to P, I V \to R$

$I \to R, I I \to T, I I I \to S, I V \to P$

$I \to T, I I \to R, I I I \to S, I V \to Q$

$I \to T, I I \to Q, I I I \to R, I V \to S$

answer is C.

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Detailed Solution

$\bar{a} . \bar{b} = (3 i + 2 j + 3 k) (4 i - 3 j) = 12 - 6 = 6$
$\bar{a} \times \bar{b} = | \begin{matrix} i & j & k \\ 3 & 2 & 3 \\ 4 & - 3 & 0 \end{matrix} | = i (0 + 9) - j (0 - 12) + k (- 9 - 8)$
$\bar{a} \times \bar{b} = 9 i + 12 j - 17 k$
$\bar{c} . \bar{d} = 12$

$\bar{c} \times \bar{d} = - 3 \hat{i} + \hat{j} + 4 \hat{k}$

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	List-I		List-II
I)	$\vec{a} . \vec{b} =$	P)	$4 \hat{i} - 3 \hat{j}$
II)	$\vec{a} \times \vec{b} =$	Q)	12
III)	$\vec{c} \times \vec{d} =$	R)	$9 \hat{i} + 12 \hat{j} - 17 \hat{k}$
IV)	$\vec{c} . \vec{d} =$	S)	$- 3 \hat{i} + \hat{j} + 4 \hat{k}$
		T)	6

If a→=3i^+2j^+3k^ , b→=4i^−3j^ , c→=i^+3j^ and d→=4j^−k^ then , List-I List-III)a→.b→=P)4i^−3j^II)a→×b→=Q)12III)c→×d→=R)9i^+12j^−17k^IV)c→.d→=S)−3i^+j^+4k^ T)6Which of the following option is correct

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