Let a = î + 2ĵ − 3k̂ and b = 2î − 3ĵ + 5k̂. If r × a = b × r, r.(αî + 2ĵ + k̂) = 3 and r.(2î + 5ĵ − αk̂) = −1, α ∈ R, then the value of α + |r|² is equal to:

Question

Accepted Answer

15. r x a = b x r means r x a = -(r x b), so r x (a+b) = 0 and r is parallel to a+b = (3,-1,2); write r = t(3,-1,2). The conditions r.(alpha,2,1)=3 and r.(2,5,-alpha)=-1 give t=1, alpha=1, so |r|^2 = 9+1+4 = 14 and alpha + |r|^2 = 15.

Let a = î + 2ĵ − 3k̂ and b = 2î − 3ĵ + 5k̂. If r × a = b × r, r.(αî + 2ĵ + k̂) = 3 and r.(2î + 5ĵ − αk̂) = −1, α ∈ R, then the value of α + |r|² is equal to:

Solution

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