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MHT CET202416 May 2024Morning ShiftMathematicsVector AlgebraActual

Let the vectors a , b , c be such that | a |=2 ;| b |=4 and | c |=4 . If the projection of b on a is equal to the projection of c on a and b is perpendicular to c , then the value of | a + b - c | is

Options

  1. A2 5
  2. B6
  3. C4
  4. D4 2

Correct answer

B. 6

Step-by-step solution

| a |=2,| ~b |=4,| c |=4 According to the given condition, Projection of b on a = projection of c on a aligned & b a | a | = c a | a | & b a = c a & ( ~b - c ) a =0...(i) aligned Now, | a + b - c |= | a + b - c |^2 = | a |^2+| b - c |^2+2 a ( b - c ) = (2)^2+| b - c |^2+2(0) ...[From (i)] = 4+| b - c |^2 = 4+| b |^2+| c |^2-2( b c ) aligned & = 4+4^2+4^2-2(0) & = 36 =6 aligned ...[ b is perpendicular to c ]

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