NDA2019MathematicsThree Dimensional GeometryActual

If the position vectors of points A and B are 3 i -2 j + k and 2 i +4 j -3 k respectively, then what is the length of A B ?

Options

Correct answer

D. 53

Step-by-step solution

Given, O A =3 i -2 j + k aligned & O B =2 i +4 j -3 k & A B = O B - O A & =(2 i +4 j -3 k )-(3 i -2 j + k ) & = i (2-3)+ j (4+2)+ k (-3-1) & =- i +6 j -4 k aligned aligned & Length of A B= (-1)^2+(6)^2+(-4)^2 & = 1+36+16 = 53 aligned

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