document.write( "Question 1203668: Let e1 = (1, 0, 0), e2 = (0, 1, 0), e3 = (0, 0, 1) ∈ R 3. Find all real numbers c ∈ 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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Algebra.Com's Answer #839410 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Let e1 = (1, 0, 0), e2 = (0, 1, 0), e3 = (0, 0, 1) ∈ $\"R%5E3\"$ $\"highlight%28cross%283%29%29\"$ . Find all real numbers $\"highlight%28cross%28c%29%29\"$ k ∈ R such that the angle between
\n" ); document.write( "the vectors −e1 + 2e2 + ke3 and −e1 + ke2 + 2e3 is π/2 (they are orthogonal).
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document.write( "The given vectors are (-1,2,k) and (-1,k,2), in coordinate form.\r\n" );
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document.write( "They are orthogonal (perpendicular) if and only if their scalar product is zero.\r\n" );
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document.write( "Find the scalar product of these vectors, using their coordinate forms.\r\n" );
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document.write( "The scalsr product is  (-1)*(-1) + 2k + 2k = 1 + 4k.\r\n" );
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document.write( "The vectors are orthogonal in  if and only if\r\n" );
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document.write( "    1 + 4k = 0,  or  k = .    ANSWER\r\n" );
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