If the given vectors (-bc, b^2 + bc, c^2 + bc | vedclass

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(B) Three vectors are coplanar if their scalar triple product is zero,which is equivalent to the determinant of the matrix formed by these vectors bei

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$bc + ca + ab = 0$

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(B) Three vectors are coplanar if their scalar triple product is zero,which is equivalent to the determinant of the matrix formed by these vectors being zero.Let the determinant be $D = \begin{vmatrix} -bc & b^2 + bc & c^2 + bc \ a^2 + ac & -ac & c^2 + ac \ a^2 + ab & b^2 + ab & -ab \end{vmatrix} = 0$.Dividing the rows by $a, b, c$ respectively (or factoring out $a, b, c$ from columns),we simplify the determinant.Factoring $a$ from the first column,$b$ from the second,and $c$ from the third,we get:$abc \begin{vmatrix} -c & b+c & c+b \ a+c & -c & c+a \ a+b & b+a & -b \end{vmatrix} = 0$.After performing row and column operations,the determinant simplifies to $(ab + bc + ca)^3 = 0$.Thus,$ab + bc + ca = 0$.

If the given vectors $(-bc, b^2 + bc, c^2 + bc)$,$(a^2 + ac, -ac, c^2 + ac)$ and $(a^2 + ab, b^2 + ab, -ab)$ are coplanar,where none of $a, b$ and $c$ is zero,then:

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