Match List-I with List-II and select the correct answer using the code given below the listsList - IList - IIP- Volume of parallelepiped determined by vectors a-b- and c- is 2- Then the volume of the parallelepiped determined by vectors 2a-b-3b-c- and c-a- is1- 100Q- Volume of parallelepiped determined by vectors a-b- and c- is 5- Then the volume of the parallelepiped determined by vectors 3a-b-b-c- and2c-a- is2- 30R- Area of a triangle with adjacent sides determined by vectors a- and b- is 20- Then the area of the triangle with adjacent sides determined by vectors 3- 24S- Area of a parallelogram with adjacent sides determined by vectors a- and b- is 30- Then the area of the parallelogram with adjacent sides determined by vectors a-b- and a- is 4- 60

(P) Given, [a⃗ b⃗ c⃗]=2 Now, V=[2(a⃗×b⃗) (3(b⃗×c⃗) c⃗×a⃗] =6[a⃗ b⃗ c⃗]^2 =24 (Q) Given, [a⃗ b⃗ c⃗]=5 Now, V=[3(a⃗+b⃗) b⃗+c⃗ 2(c⃗+a⃗)] =6[a⃗+b⃗ b⃗+c⃗ c⃗+ ...

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 List-II and select the correct answer using the code given below the lists

List - I List - II

P. Volume of parallelepiped determined by vectors $\to a, \to b and \to c$ is 2. Then the volume 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 1. 100

Q. Volume of parallelepiped determined by vectors $\to a, \to b and \to c$ is 5. Then the volume of the parallelepiped determined by vectors $3 (\to a + \to b), (\to b + \to c) and 2 (\to c + \to a)$ is 2. 30

R. Area of a triangle with adjacent sides determined by vectors $\to a and \to b$ is 20. Then the area of the triangle with adjacent sides determined by vectors 3. 24

S. Area of a parallelogram with adjacent sides determined by vectors $\to a and \to b$ is 30. Then the area of the parallelogram with adjacent sides determined by vectors $(\to a + \to b) and \to a$ is 4. 60

P Q R S
3 4 1 2

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

P Q R S
2 3 1 4

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

P Q R S
1 4 3 2

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

P Q R S
4 2 3 1

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

Open in App

Solution

The correct option is A P Q R S
3 4 1 2
(P) Given, $[\to a \to b \to c] = 2$

Now, $V = [2 (\to a \times \to b) (3 (\to b \times \to c) \to c \times \to a]$

$= 6 [\to a \to b \to c]^{2}$

$= 24$

(Q) Given, $[\to a \to b \to c] = 5$

Now, $V = [3 (\to a + \to b) \to b + \to c 2 (\to c + \to a)]$

$= 6 [\to a + \to b \to b + \to c \to c + \to a]$

$= 12 [\to a \to b \to c]$

$= 60$

(R) Given, $| \to a \times \to b | = 40$

Now, $A = \frac{1}{2} | (2 \to a + 3 \to b) \times (\to a \times \to b) |$

$= \frac{1}{2} .5 | \to a + \to b |$

$= \frac{5}{2} \times 40$

$= 100$

(S) Given, $| \to a \times \to b | = 30$

Now, $A = | (\to a + \to b) \times \to a |$

$= | \to a + \to b |$

$= 30$

Suggest Corrections

Similar questions

Q. Match List 1 with List 2

	List 1		List 2
A.	The volume of the parallelopiped determined by vectors $\to a, \to b$ and $\to c$ is 2. Then, the volume of the parallelopiped determined by vectors $2 (\to a \times \to b), 3 (\to b \times \to c)$ and $(\to c \times \to a)$ is	1.	$100$
B.	The volume of the parallelopiped determined by vectors $\to a, \to b$ and $\to c$ is 5. Then, the volume of the parallelopiped determined by vectors $3 (\to a + \to b), (\to b + \to c)$ and $2 (\to c + \to a)$ is	2.	$30$
C.	The area of a triangle with adjacent sides determined by vectors $\to a$ and $\to b$ is 20. Then, the area of the triangle with adjacent sides determined by vectors $(2 \to a + 3 \to b)$ and $(\to a - \to b)$ is	3.	$24$
D.	The area of a parallelogram with adjacent sides determined by vectors $\to a$ and $\to b$ is $30$ . Then, the area of the parallelogram with adjacent sides determined by vectors $(\to a + \to b)$ and $\to a$ is	4.	$60$

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. If

\to a

and

\to b

are the vectors determined by two adjacent sides of regular hexagon, then vector

E F

Q. Find the area of the parallelogram whose adjacent sides are determined by the vectors

\to a = 3^i +^j + 4^k

and

\to b =^i -^j +^k

Q. Find the area of the triangle whose adjacent sides are determined by the vector

\to a = - 2^i - 5^k

and

\to b =^i - 2^j -^k

Join BYJU'S Learning Program

List - I	List - II
P. Volume of parallelepiped determined by vectors $\to a, \to b and \to c$ is 2. Then the volume 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	1. 100
Q. Volume of parallelepiped determined by vectors $\to a, \to b and \to c$ is 5. Then the volume of the parallelepiped determined by vectors $3 (\to a + \to b), (\to b + \to c) and 2 (\to c + \to a)$ is	2. 30
R. Area of a triangle with adjacent sides determined by vectors $\to a and \to b$ is 20. Then the area of the triangle with adjacent sides determined by vectors	3. 24
S. Area of a parallelogram with adjacent sides determined by vectors $\to a and \to b$ is 30. Then the area of the parallelogram with adjacent sides determined by vectors $(\to a + \to b) and \to a$ is	4. 60