Vectors · Cross product and collinear vectors

Let

\vec c

and

\vec d

be vectors such that

\lvert\vec c + \vec d\rvert = \sqrt{29}

and

\vec c\times(2\hat i + 3\hat j + 4\hat k) = (2\hat i + 3\hat j + 4\hat k)\times\vec d

. If

\lambda_1, \lambda_2\ (\lambda_1 > \lambda_2)

are the possible values of

(\vec c + \vec d)\cdot(-7\hat i + 2\hat j + 3\hat k)

, then the equation

K^2x^2 + (K^2 - 5K + \lambda_1)xy + \left(3K + \dfrac{\lambda_2}{2}\right)y^2 - 8x + 12y + \lambda_2 = 0

represents a circle, for

K

equal to:

We corrected a printing error in the original paper

Source printed “represents a circle, for $k$ equal to” (lower-case $k$ ; the equation uses $K$ ).

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