Question
The vector →C, directed along the internal bisector of the angle between the vectors →a=7^i−4^j−4^k and →b=−2^i−^j+2^k with |→c|=5√6, is
Answer: Option A
:
A
The required vector →C is given by
→C=λ(^a+^b)=λ(→a|→a|+→b|→b|)=λ{19(7^i−4^j−4^k)+13(−2^i−^j+2^k)}
⇒→c=λ9(^i−7^j+2^k)⇒|→c|=±λ9√1+49+4=±λ9√54
But |→c|=5√6 (given)
∴±λ9√54=5√6⇒λ=±15
Hence, →c=±159(^i−7^j+2^k)=±53(^i−7^j+2^k)
Was this answer helpful ?
:
A
The required vector →C is given by
→C=λ(^a+^b)=λ(→a|→a|+→b|→b|)=λ{19(7^i−4^j−4^k)+13(−2^i−^j+2^k)}
⇒→c=λ9(^i−7^j+2^k)⇒|→c|=±λ9√1+49+4=±λ9√54
But |→c|=5√6 (given)
∴±λ9√54=5√6⇒λ=±15
Hence, →c=±159(^i−7^j+2^k)=±53(^i−7^j+2^k)
Was this answer helpful ?
Submit Solution