JEE Advanced 2013 · Paper 2 · Mathematics Q60

MathematicsList match+3 / -1Question 60 of 60

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

List I

P
Volume of parallelepiped determined by vectors $\vec a$ , $\vec b$ and $\vec c$ is 2. Then the volume of the parallelepiped determined by vectors $2(\vec a\times\vec b)$ , $3(\vec b\times\vec c)$ and $(\vec c\times\vec a)$ is
Q
Volume of parallelepiped determined by vectors $\vec a$ , $\vec b$ and $\vec c$ is 5. Then the volume of the parallelepiped determined by vectors $3(\vec a+\vec b)$ , $(\vec b+\vec c)$ and $2(\vec c+\vec a)$ is
R
Area of a triangle with adjacent sides determined by vectors $\vec a$ and $\vec b$ is 20. Then the area of the triangle with adjacent sides determined by vectors $(2\vec a+3\vec b)$ and $(\vec a-\vec b)$ is
S
Area of a parallelogram with adjacent sides determined by vectors $\vec a$ and $\vec b$ is 30. Then the area of the parallelogram with adjacent sides determined by vectors $(\vec a+\vec b)$ and $\vec a$ is

List II

P → 4; Q → 2; R → 3; S → 1

P → 2; Q → 3; R → 1; S → 4

P → 3; Q → 4; R → 1; S → 2

P → 1; Q → 4; R → 3; S → 2

Answer and worked solution

Official answer: C

P: $[\vec a\times\vec b,\ \vec b\times\vec c,\ \vec c\times\vec a]=[\vec a\,\vec b\,\vec c]^2=4$ ; with the factors $2\cdot3$ : 24. → 3
Q: $[\vec a+\vec b,\ \vec b+\vec c,\ \vec c+\vec a]=2[\vec a\,\vec b\,\vec c]=10$ ; with $3\cdot2$ : 60. → 4
R: $(2\vec a+3\vec b)\times(\vec a-\vec b)=-5\,\vec a\times\vec b$ : area $5\times20=100$ . → 1
S: $(\vec a+\vec b)\times\vec a=\vec b\times\vec a$ : area 30. → 2

Code 3 4 1 2.

(C)

Topics:Scalar and vector triple products Cross product

JEE Advanced 2013 · Paper 2, Mathematics question 60