Question

The vector c directed along the internal bisector of the angle between the vectors a = 7i - 4j - 4k and b = -2i - j + 2k with |c| = 5√6 ?

Answer 1

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)