Question 1203668
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Let e1 = (1, 0, 0), e2 = (0, 1, 0), e3 = (0, 0, 1) ∈ {{{R^3}}} {{{highlight(cross(3))}}}. Find all real numbers {{{highlight(cross(c))}}} k ∈ R such that the angle between 
the vectors −e1 + 2e2 + ke3 and −e1 + ke2 + 2e3 is π/2 (they are orthogonal).
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<pre>
The given vectors are (-1,2,k) and (-1,k,2), in coordinate form.


They are orthogonal (perpendicular) if and only if their scalar product is zero.

Find the scalar product of these vectors, using their coordinate forms.

The scalsr product is  (-1)*(-1) + 2k + 2k = 1 + 4k.


The vectors are orthogonal in {{{R^3}}} if and only if

    1 + 4k = 0,  or  k = {{{-1/4}}}.    <U>ANSWER</U>
</pre>

Solved.