Let →a=^i+2^j+4^k, →b=^i+λ^j+4^k and →c=2^i+4^j+(λ^2-1)^k be coplanar vectors. Then the non-zero vector →a × →c is:

As a, b, c are co-planar vectors [→a →b →c]=0
→
∣∣∣
1 2 4
1 λ 4
2 4 λ^2-1
∣∣∣=0
→λ(λ^2-1)-8-(2(λ^2-1)-8λ)+8(4-2λ)=0
→λ^3-λ-8-2λ^2+2+8λ+32-16λ=0
→λ^3-2λ^2-9λ+26=0
→λ^3-2λ^2-18λ+26=0
→(λ-2)(λ^2-8)=0
→λ=2, λ=±√8
If λ = 2, then →c=2^i+4^j+3^k and →a=^i+2^j+4^k so →a is not parallel to →c
Hence λ=2
Then →a × →c=∣∣∣^i ^j ^k1 2 42 4 3∣∣∣=0^i+5^j