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Question
The triangle ABC is defined by the vertices A(1,−2,2),B(1,4,0) and C(−4,1,1). Let M be the root of the altitude drawn from the vertices B to side AC. Then −−→BM=
The triangle ABC is defined by the vertices A(1,−2,2),B(1,4,0) and C(−4,1,1). Let M be the root of the altitude drawn from the vertices B to side AC. Then −−→BM=
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Solution
The correct option is B (−207,−307,107)
−−→MB=−−→AB−−−→AM=−−→AB−(−−→AB.−−→AC)−−→AC(−−−→|AC|)2=(6→j−2→k)−(6→j−2→k).(5→i+3→j−→k)(−5→i+3→j−→k)(25+9+1)=(6→j−2→k)−2035(−5→i+3→j−→k) =107(2→i+3→j−k)∴−−→BM=−107(2→i+3→j−→k)=(−207→i−307→j+107→k)
−−→MB=−−→AB−−−→AM=−−→AB−(−−→AB.−−→AC)−−→AC(−−−→|AC|)2
=(6→j−2→k)−(6→j−2→k).(5→i+3→j−→k)(−5→i+3→j−→k)(25+9+1)
=(6→j−2→k)−2035(−5→i+3→j−→k) =107(2→i+3→j−k)
∴−−→BM=−107(2→i+3→j−→k)=(−207→i−307→j+107→k)
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