Match List I with the List II and select the correct answer using the code given below the lists - List I List II- A Volume of parallelepiped determined by vectors a-b and c is 2-Then the volume P 100- of the parallelepiped determined by vectors 2a-b-3b-c and c-a is- B Volume of parallelepiped determined by vectors a-b and c is 5-Then the volume Q 30- of the parallelepiped determined by vectors 3a- b-b- c and 2c - a is- C Area of a triangle with adjacent sides determined by vectors a-b is 20- Then the R 24- area of the triangle with adjacent sides determined by vectors 2a- 3b and a-b is- D Area of a parallelogram with adjacent sides determined by vectors a and b is 30- S 60- Then the area of the parallelogram with adjacent sides determined by vectors- a- b and a is- -Which of the following is the only CORRECT combination-

(A) [a b c]=2 ∴[2(a×b) 3(b×c) (c×a)]=2(a×b) ·[3(b×c) ×(c×a)] =6(a×b) ·[d×(c×a)](let d=b×c) =6(a×b) ·[(d·a)c (d·c)a] =6[a b c](d ·a) 6[a b 0](d·c) =6[a b c][b c ...

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

Byju's Answer

Standard XII

Physics

Vectors and Its Types

Match List I ...

Question

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

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

Which of the following is the only CORRECT combination?

(A) \to (S), (B) \to (Q), (C) \to (R), (B) \to (P)

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

(A) \to (Q), (B) \to (R), (C) \to (P), (B) \to (S)

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

(A) \to (R), (B) \to (S), (C) \to (P), (B) \to (Q)

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

(A) \to (P), (B) \to (S), (C) \to (R), (B) \to (Q)

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

Open in App

Solution

The correct option is C $(A) \to (R), (B) \to (S), (C) \to (P), (B) \to (Q)$
$(A)$
$[\to a \to b \to c] = 2$
$∴ [2 (\to a \times \to b) 3 (\to b \times \to c) (\to c \times \to a)] = 2 (\to a \times \to b) \cdot [3 (\to b \times \to c) \times (\to c \times \to a)]$
$= 6 (\to a \times \to b) \cdot [\to d \times (\to c \times \to a)]$ (let $\to d = \to b \times \to c$ )
$= 6 (\to a \times \to b) \cdot [(\to d \cdot \to a) \to c - (\to d \cdot \to c) \to a]$
$= 6 [\to a \to b \to c] (d \cdot \to a) - 6 [\to a \to b 0] (\to d \cdot \to c)$
$= 6 [\to a \to b \to c] [\to b \to c \to a]$
$= 6 {[\to a \to b \to c]}^{2} = 24$

$(B)$
$[\to a \to b \to c] = 5$
$∴ [3 (\to a + \to b) (\to b + \to c) 2 (\to c + \to a)] = 3 (\to a + \to b) \cdot [(\to b + \to c) \times 2 (\to c + \to a)]$
$= 6 (\to a + \to b) \cdot [(\to b \times \to c) + (\to b \times \to a) + (\to c \times \to c) + (\to c \times \to a)]$
$= 6 [\to a \to b \to c] + 6 [\to a \to b \to c]$
$= 12 [\to a \to b \to c] = 60$

$(C)$
$\frac{1}{2} ∣ ∣ ∣ \to a \times \to b ∣ ∣ ∣ = 20$
$∴ \frac{1}{2} ∣ ∣ ∣ (2 \to a + 3 \to b) \times (\to a - \to b) ∣ ∣ ∣ = \frac{1}{2} ∣ ∣ ∣ - 2 (\to a \times \to b) + 3 (\to b \times \to a) ∣ ∣ ∣$
$= \frac{1}{2} ∣ ∣ ∣ 5 (\to b \times \to a) ∣ ∣ ∣$
$= 5 \times 20 = 100$

$(D)$
$∣ ∣ ∣ \to a \times \to b ∣ ∣ ∣ = 30$
$∴ ∣ ∣ ∣ (\to a + \to b) \times \to a ∣ ∣ ∣ = ∣ ∣ ∣ \to a \times \to a + \to b \times \to a ∣ ∣ ∣$
$= 30$

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. Volume of parallelopiped formed by vectors

\to a \times \to b, \to b \times \to c

and

\to c \times \to a

36

cubic units. Based on the given information above match the following by appropriately matching the lists given in Column I and Column II.

\begin{matrix} C o l u m n 1 & C o l u m n 2 a. Volume of parallelopiped formed by vectors & p. 0 cubic units \to a, \to b and \to c is b. Volume of tetrahedron formed by vectors & q. 12 cubic units \to a, \to b and \to c is c. Volume of parallelopiped formed by vectors & r. 6 cubic units \to a + \to b, \to b + \to c and \to c + \to a is d. Volume of parallelopiped formed by vectors & s. 1 cubic unit \to a - \to b, \to b - \to c and \to c - \to a is \end{matrix}

If $\to a$ and $\to b$ are two vectors such that $| \to a | = 3, | \to b | = 2$ and angle between $\to a$ and $\to b is \frac{π}{3},$ then the area of the triangle with adjacent sides $\to a + 2 \to b$ and $2 \to a + \to b$ in sq. units is