Match List I with the List II and select the correct answer using the code given below the lists -egin array -1- hlineWline- text the triangle with adjacent sides determined by 3 a -4 b and a -3 b is Wline- text Q -text9 1- -extparallelopiped determined by vectors 3 a - b - b - c - 4 c - aWlineWline

The correct option is D (C)→(S),(D)→(Q)(C) Given, |a×b|=8 ∴ |(2a b)×b| =2|a×b|=16 (D) Given, 16[a b c]=12 ⇒[a b c]=3 ∴16[2(a×b) 3(b×c) (c×a) ] =[a×b ...

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Byju's Answer

Standard XII

Mathematics

Applications Scalar Triple Product

Match List I ...

Question

Match $List I$ with the $List II$ and select the correct answer using the code given below the lists :

$\begin{matrix} List I & List II (A) & Area of a triangle with adjacent sides determined by vectors \to a and \to b is 1 . Then the area of & (P) & 6 the triangle with adjacent sides determined by (3 \to a + 4 \to b) and (\to a - 3 \to b) is (B) & Volume of parallelopiped determined by vectors \to a, \to b, \to c is \frac{1}{4} . Then the volume of the & (Q) & 9 parallelopiped determined by vectors 3 (\to a + \to b), (\to b + \to c), 4 (\to c + \to a) is (C) & Area of a parallelogram with adjacent sides determined by vectors \to a and \to b is 8 . Then the & (R) & 13 area of the parallelogram with adjacent sides determined by vectors (2 \to a - \to b) and \to b is (D) & Volume of tetrahedron determined by vectors \to a, \to b and \to c is \frac{1}{2} . Then the volume of the & (S) & 16 tetrahedron determined by vectors 2 (\to a \times \to b), 3 (\to b \times \to c) and (\to c \times \to a) is \end{matrix}$

Which of the following is the only CORRECT combination?

(C) \to (R), (D) \to (P)

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(C) \to (Q), (D) \to (P)

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(C) \to (P), (D) \to (S)

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(C) \to (S), (D) \to (Q)

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Solution

The correct option is D $(C) \to (S), (D) \to (Q)$
$(C)$
Given, $| \to a \times \to b | = 8$
$∴ | (2 \to a - \to b) \times \to b |$
$= 2 | \to a \times \to b | = 16$

$(D)$
Given, $\frac{1}{6} [\to a \to b \to c] = \frac{1}{2}$
$\Rightarrow [\to a \to b \to c] = 3$
$∴ \frac{1}{6} [2 (\to a \times \to b) 3 (\to b \times \to c) (\to c \times \to a)]$
$= [\to a \times \to b \to b \times \to c \to c \times \to a]$
$= {[\to a \to b \to c]}^{2} = 9$

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Similar questions

Q. Match

List I

with the

List II

and select the correct answer using the code given below the lists :

\begin{matrix} List I & List II (A) & Area of a triangle with adjacent sides determined by vectors \to a and \to b is 1 . Then the area of & (P) & 6 the triangle with adjacent sides determined by (3 \to a + 4 \to b) and (\to a - 3 \to b) is (B) & Volume of parallelopiped determined by vectors \to a, \to b, \to c is \frac{1}{4} . Then the volume of the & (Q) & 9 parallelopiped determined by vectors 3 (\to a + \to b), (\to b + \to c), 4 (\to c + \to a) is (C) & Area of a parallelogram with adjacent sides determined by vectors \to a and \to b is 8 . Then the & (R) & 13 area of the parallelogram with adjacent sides determined by vectors (2 \to a - \to b) and \to b is (D) & Volume of tetrahedron determined by vectors \to a, \to b and \to c is \frac{1}{2} . Then the volume of the & (S) & 16 tetrahedron determined by vectors 2 (\to a \times \to b), 3 (\to b \times \to c) and (\to c \times \to a) is \end{matrix}

Which of the following is the only CORRECT combination?

Q. Match

List I

with the

List II

and select the correct answer using the code given below the lists :

\begin{matrix} List I & List II (A) & Volume of parallelepiped determined by vectors \to a, \to b and \to c is 2. Then the volume & (P) & 100 of the parallelepiped determined by vectors 2 (\to a \times \to b), 3 (\to b \times \to c) and (\to c \times \to a) is (B) & Volume of parallelepiped determined by vectors \to a, \to b and \to c is 5. Then the volume & (Q) & 30 of the parallelepiped determined by vectors 3 (\to a + \to b), (\to b + \to c) and 2 (\to c + \to a) is (C) & Area of a triangle with adjacent sides determined by vectors \to a, \to b is 20. Then the & (R) & 24 area of the triangle with adjacent sides determined by vectors (2 \to a + 3 \to b) and (\to a - \to b) is (D) & Area of a parallelogram with adjacent sides determined by vectors \to a and \to b is 30. & (S) & 60 Then the area of the parallelogram with adjacent sides determined by vectors (\to a + \to b) and \to a is \end{matrix}

Which of the following is the only CORRECT combination?

Q. Match

List I

with

List II

and select the correct answer using the code given below the lists :

\begin{matrix} List I & List II (A) & In a △ A B C, if a^{2} + b^{2} + c^{2} = a b + b c + c a, then & (P) & △ A B C is an equilateral triangle (B) & In a △ A B C, if a^{2} + 2 b^{2} + c^{2} = 2 b c + 2 a b, then & (Q) & △ A B C is a right angled triangle (C) & In a △ A B C, if a^{2} + b^{2} + c^{2} = \sqrt{2} a (b + c), then & (R) & △ A B C is a scalene triangle (D) & In a △ A B C, if a^{2} + b^{2} + c^{2} = c a + \sqrt{3} a b, then & (S) & A = 90^{\circ}, B = 45^{\circ}, C = 45^{\circ} \end{matrix}

Which of the following is the only CORRECT combination?

Match the List -I with List -II and select correct answer by using the codes given below the lists.

Q. Match List I with List II and select the correct answer by using the codes given below the lists.
List I List II
A. Fruit 1. Ovule
B. Seed 2. Leaf
C. Wood 3. Stem
D. Starch 4. Ovary

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The correct option is D (C)→(S),(D)→(Q)(C) Given, |→a×→b|=8 ∴|(2→a−→b)×→b| =2|→a×→b|=16 (D) Given, 16[→a →b →c]=12 ⇒[→a →b →c]=3 ∴16[2(→a×→b) 3(→b×→c) (→c×→a)] =[→a×→b →b×→c →c×→a] =[→a →b →c]2=9