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Most Important Selected Qs for JEE AdvancedMathematicsVector Algebra

Which of the following statement(s) is/are correct :

Options

  1. AIf a , b , c are non-coplanar and d is any vector, then [ d b c ] a +[ d c a ] b +[ d a b ] c -[ a b c ] d = 0
  2. BIf I is incentre of A B C then | B C | I A +| C A | I B +| A B | I C = 0
  3. CAny vector in three dimension can be written as linear combination of three non-coplanar vectors.
  4. DIn a triangle, if position vector of vertices are a , b , c , then position vector of incentre is a + b + c 3

Correct answer

C. Any vector in three dimension can be written as linear combination of three non-coplanar vectors.

Step-by-step solution

(A) aligned & [ d b c ] a +[ d c a ] b +[ d a b ] c -[ a b c ] d &=([ b c d ] a -[ b c a ] d )+([ d a b ] c -[ d a c ] b )=( b c ) ( a d )+( d a ) ( c b ) &=( d a ) ( b c )-( d a ) ( b c )= 0 aligned I a a +b b +c c a+b+c

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