MHT CET202416 May 2024Evening ShiftMathematicsVector AlgebraActual

If a =2 i - j + k , b = i + j -2 k and c =4 i -2 j + k , then the unit vector in the direction of 3 a + b -2 c is

Options

A1 6 (- i +2 j - k )
B1 6 ( i +2 j + k )
C1 6 (2 i - j - k )
D1 6 (- i -2 j + k )

Correct answer

A. 1 6 (- i +2 j - k )

Step-by-step solution

aligned & 3 a + b -2 c & =3(2 i - j + k )+( i + j -2 k )-2(4 i -2 j + k ) & =-( i +2 j - k aligned The unit vector in the direction of 3 a + b -2 c is aligned & - i +2 j - k | - i +2 j - k | & = - i +2 j - k (-1)^2+2^2+(-1)^2 & = 1 6 (- i +2 j - k ) aligned

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