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Vector Algebra question

2013 · Shift 2 · Q21
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  5. /2013 · Shift 2 · Q21

Vector Algebra question

2013 · Shift 2 · Q21

JEE AdvancedMathematicsVector AlgebraMCQ+4 / −1
match List III with List IIIIII and select the correct answer using the code given below the lists:             \,\,\,\,\,\,\,\,\,\,\,\, List III (P.)     \,\,\,\, Volume of parallelopiped determined by vectors a→,b→\overrightarrow a ,\overrightarrow ba,b and c→\overrightarrow cc is 2.2.2. Then the volume of the parallelepiped determined by vectors 2(a→×b→),3(b→×c→)2\left( {\overrightarrow a \times \overrightarrow b } \right),3\left( {\overrightarrow b \times \overrightarrow c } \right)2(a×b),3(b×c) and (c→×a→)\left( {\overrightarrow c \times \overrightarrow a } \right)(c×a) is (Q.)     \,\,\,\, Volume of parallelopiped determined by vectors a→,b→\overrightarrow a ,\overrightarrow ba,b and c→\overrightarrow cc is 5.5.5. Then the volume of the parallelepiped determined by vectors 3(a→+b→),(b→+c→)3\left( {\overrightarrow a + \overrightarrow b } \right),\left( {\overrightarrow b + \overrightarrow c } \right)3(a+b),(b+c) and 2(c→+a→)2\left( {\overrightarrow c + \overrightarrow a } \right)2(c+a) is (R.)     \,\,\,\, Area of a triangle with adjacent sides determined by vectors a→{\overrightarrow a }a and b→{\overrightarrow b }b is 20.20.20. Then the area of the triangle with adjacent sides determined by vectors (2a→+3b→)\left( {2\overrightarrow a + 3\overrightarrow b } \right)(2a+3b) and (a→−b→)\left( {\overrightarrow a - \overrightarrow b } \right)(a−b) is (S.)     \,\,\,\, Area of a parallelogram with adjacent sides determined by vectors a→{\overrightarrow a }a and b→{\overrightarrow b }b is 30.30.30. Then the area of the parallelogram with adjacent sides determined by vectors (a→+b→)\left( {\overrightarrow a + \overrightarrow b } \right)(a+b) and a→{\overrightarrow a }a is             \,\,\,\,\,\,\,\,\,\,\,\, List IIIIII (1.)     100\,\,\,\,100100 (2.)     30\,\,\,\,3030 (3.)     24\,\,\,\,2424 (4.)     60\,\,\,\,6060
  1. A
    P=4,Q=2,R=3,S=1P = 4,Q = 2,R = 3,S = 1P=4,Q=2,R=3,S=1
  2. B
    P=2,Q=3,R=1,S=4P = 2,Q = 3,R = 1,S = 4P=2,Q=3,R=1,S=4
  3. C
    P=3,Q=4,R=1,S=2P = 3,Q = 4,R = 1,S = 2P=3,Q=4,R=1,S=2
  4. D
    P=1,Q=4,R=3,S=2P = 1,Q = 4,R = 3,S = 2P=1,Q=4,R=3,S=2
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