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AP EAMCET202315 May 2023Evening ShiftMathematicsVector AlgebraActual

Let ( a , b ) denote the angle between vectors a and b . If a =2 i +3 j +6 k , a b =4 and ( a , b )= ⁻¹ ( 4 21 ) , then a + b =

Options

  1. A3 i + j +8 k
  2. B3 i +5 j +4 k
  3. C3 i +5 j +8 k
  4. Di + j +8 k

Correct answer

D. i + j +8 k

Step-by-step solution

aligned & a =2 i +3 j +6 k | a |=7 & a b =4 & | a | | b | =4 & 7 | b | 4 21 =4 & 7 | b | 1 21 =1 | b |=3 . & | a + b |^2=| a |^2+| b |^2+2 a b & | a + b |^2=49+9+2 4=66 & | a + b |^2= 66 . aligned Let us check option (a) : | a + b |= (3)^2+1+64 66 (not correct) Let us check option (b) : | a + b |= 9+25+16 66 (not correct) Let us check option (c) : | a + b |= 9+25+64 66 (not correct) Let us check option (d) : | a + b |= 1+1+64 = 66 (correct)

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