The value of ,λ, if the volume of a tetrahedron whose vertices are with position vectors i^−6j^+10k^,−i^−3j^+7k^,5i^−j^+λk^ and 7i^−4j^+7k^ is 11 cubic unit.

Let the vertices be A, B, C, D and O be the origin. ∴     OA→=i^−6j^+10k^,OB→=i^−3j^+7k^    OC→=−5i^−j^+λk^, OD→=7i^−4j^+7k^∴     AB→=OB→−OA→=−2i^+3j^−3k^    AC→=OC→−OA→=4i^+5j^+(λ−10)k^AD→=OD→−OA→=6i^+2j^−3k^Volume of tetrahedron=16[AB→AC→AD→]=16−23−345λ−1062−3=16{−2(−15−2λ+20)−3(−12−6λ+60)−3(8−30)}=16{4λ−10−144+18λ+66}=16(22λ−88)=11 or  2λ−8=6or  λ=7