Two vectors are perpendicular when their dot product equals zero.
A⋅B=0
A=2i^−j^+2k^
B=3i^+λj^+k^
The dot product is found by multiplying matching components and adding them:
A⋅B=(a1×b1)+(a2×b2)+(a3×b3)
=(2)(3)+(−1)(λ)+(2)(1)
=6−λ+2
=8−λ
Since the vectors are perpendicular:
8−λ=0
λ=8