The line of intersection of the planes r cdot | vedclass

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Question

(B) The line of intersection of the planes $r \cdot (i - 3j + k) = 1$ and $r \cdot (2i + 5j - 3k) = 2$ is perpendicular to each of the normal vectors

Vedclass · Accepted Answer

$4i + 5j + 11k$

Vedclass · Answer

(B) The line of intersection of the planes $r \cdot (i - 3j + k) = 1$ and $r \cdot (2i + 5j - 3k) = 2$ is perpendicular to each of the normal vectors $n_1 = i - 3j + k$ and $n_2 = 2i + 5j - 3k$.Therefore,the line is parallel to the vector $n_1 	imes n_2$.$n_1 	imes n_2 = \begin{vmatrix} i & j & k \ 1 & -3 & 1 \ 2 & 5 & -3 \end{vmatrix}$$= i((-3)(-3) - (1)(5)) - j((1)(-3) - (1)(2)) + k((1)(5) - (-3)(2))$$= i(9 - 5) - j(-3 - 2) + k(5 + 6)$$= 4i + 5j + 11k$.

The line of intersection of the planes $r \cdot (i - 3j + k) = 1$ and $r \cdot (2i + 5j - 3k) = 2$ is parallel to the vector

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