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Let the position vectors ofthe points `Pa n dQ`be `4 hat i+ hat j+lambda hat ka n d2 hat i- hat j+lambda hat k ,`respectively. Vector ` hat i- hat j+6 hat k`is perpendicular to theplane containing the origin and the points`Pa n dQ`. Then `lambda`equals`1//2`b. `1//2`c. `1`d. none of theseA. `-1//2`B. `1//2`C. 1D. none of these |
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Answer» Correct Answer - a A vector perpendicular to the plane of O , P and Q is ` vec(OP) xx vec(OQ) ` Now, `vec(OP) xx vec(OQ) = |{:(hati,hatj,hatk),(4,1,lambda),(2,-1,lambda):}|` ` = 2lambda hati - 2hatj - 6hatk` therefore, `hatim -hatj + 6hatk` is parallel to `2lambda hati - 2lambdahatj - 6hatk` Hence, `1/(2lambda) = (-1)/(-2lambda) = 6/(-6)` `lambda = -1/2` |
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