Question

Find the lambda so that the vectors 2i-4j+5k , i-lambda j+ k and 3i+2j-5k are coplaner

Answer 1

Answer:

Step-by-step explanation:

For 3 vectors to be coplanar, their scalar triple product must be zero

Given vectors,

a = 2i-4j+5k

b= i-λj+k

c= 3i+2j-5k

Thus for coplanarity, [a b c] =0

or$\left[\begin{array}{ccc}2&-4&5\\1&-λ&1\\3&2&-5\end{array}\right]$

or 2( 5λ-2) + 4(-5-3) + 5(2+3λ) =0

or 10λ-4 -32+ 10 +15λ =0

or 25λ =26

or λ = 26/25