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Find the value of `lambda`, which makesthe vectors ` vec a , vec b`and ` vec c`coplanar, where ` vec a= hat i+3 hat j+4 hat k , vec b=2 hat i+lambda hat j+2 hat k`and ` vec c=4 hat i-7 hat j+10 hat k` |
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Answer» If `veca, vecb and vecc` are coplanar,`:. vecb*(vecaxxvecc) = 0` `vecaxxvecc = |[hati,hatj,hatk],[1,3,4],[4,-7,10]|` `= (30-(-28))hati - (10-16)hatj + (-7-12)hatk` `=58hati+6hatj-19hatk` Now, `vecb.(vecaxxvecc) = 0` `(2hati+lambdahatj+2hatk)*(58hati+6hatj-19hatk) = 0` `=>116+6lambda-38 = 0` `=>6lambda = -78` `=>lambda = -13` |
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