Let a⇀,b⇀ and c⇀be three non-coplanar vectors. If a⇀+2b⇀2b⇀+c⇀5c⇀+a⇀=λa⇀b→c⇀ then find λ?
10
11
12
0
Determine the value of λ
If a⇀,b⇀ and c⇀be non-coplanar vectors. then a⇀b→c→=a1a2a3b1b2b3c1c2c3≠0.
We have,
⇒a⇀+2b⇀2b⇀+c⇀5c⇀+a⇀=λa⇀b→c⇀⇒120021105a⇀b→c⇀=λa⇀b→c⇀⇒120021105a⇀b→c⇀-λa⇀b→c⇀=0⇒120021105-λa⇀b→c⇀=0⇒120021105-λ=0a⇀b→c⇀≠0,threevectorsarecoplanar⇒λ=120021105
∴λ=1(10-0)-2(0-1)+0=10+2=12
Hence, option (C) is the correct answer
If a,b,c are non-coplanar vectors and λ is a real number, then [λ(a+b)λ2bλc]=[ab+cb] for?