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 B (A)→(R),(B)→(P)(A) Given, 12|a×b|=1 ⇒ |a×b|=2 ∴12|(3a+4b)×(a 3b)| =12|13(a×b)|=13 (B) Given, [a b c]=14 ∴[3(a+b) (b+c) 4(c+a)] =12 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

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?

(A) \to (R), (B) \to (Q)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(A) \to (R), (B) \to (P)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

(A) \to (S), (B) \to (P)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(A) \to (Q), (B) \to (R)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $(A) \to (R), (B) \to (P)$
$(A)$
Given, $\frac{1}{2} | \to a \times \to b | = 1$
$\Rightarrow | \to a \times \to b | = 2$
$∴ \frac{1}{2} | (3 \to a + 4 \to b) \times (\to a - 3 \to b) |$
$= \frac{1}{2} | 13 (\to a \times \to b) | = 13$

$(B)$
Given, $[\to a \to b \to c] = \frac{1}{4}$
$∴ [3 (\to a + \to b) (\to b + \to c) 4 (\to c + \to a)]$
$= 12 (2) [\to a \to b \to c]$
$= \frac{24}{4} = 6$

Suggest Corrections

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) & 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.

Join BYJU'S Learning Program

The correct option is B (A)→(R),(B)→(P)(A) Given, 12|→a×→b|=1 ⇒|→a×→b|=2 ∴12|(3→a+4→b)×(→a−3→b)| =12|13(→a×→b)|=13 (B) Given, [→a →b →c]=14 ∴[3(→a+→b) (→b+→c) 4(→c+→a)] =12(2)[→a →b →c] =244=6