AP EAMCET202315 May 2023Evening ShiftMathematicsVector AlgebraActual

Let OA = i +2 j -2 k and OB =-2 i -3 j +6 k be the position vectors of two points A and B . If C is a point on the bisector AOB and OC = 42 , then OC =

Options

A4 i - j +5 k
Bi +5 j +4 k
C5 i +4 j + k
Di -4 j +5 k

Correct answer

B. i +5 j +4 k

Step-by-step solution

Given O A = i +2 j -2 k and O B =-2 i -3 j +6 k Now unit vector bisector A O B aligned & = i +2 j -2 k 3 (-2 i-3 j+6 k) 7 & = i +5 j +4 k 21 or 13 i +23 j -32 k 21 aligned Since (1+25+16) 441 x^2=42 x=21 So required vector = i +5 j +4 k

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