a vector = [k+2,k^2-4],    a≠0 b vector = [3,-3] Decide k so that a vector ⊥ b vector

Expert Answers
cosinusix eNotes educator| Certified Educator

The 2 vectors are orthogonal if their dot product is 0



divide the equation by 3



2 answers : k=3 or K=-2


sirishajunna | Student

two vector are said to be orthogonal if their dot product=0

if a,b are two vector then


so by given problem




since a.b should be =0 as they are orthogonal


so when we take -3 ascommon in the expression the expression is


this expression can be witten as

k^2-3k+2k-6=0           [since -3 and 2 are factors of -6]

this expression can be rewitten as



so the values of k can be k=3 or -2

but k=-2 makes a=0 but as per the condition a!=0

so k=3