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Question

The direction ratios of the line $$x-y+z-5=0=x-3y-6$$ are


A
3,1,2
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B
2,4,1
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C
314,114,214
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D
241,441,141
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Solution

The correct option is A $$3,1,-2$$

Normals of $${ P }_{ 1 },{ P }_{ 2 }$$ gives the direction ratios of line of intersection, i.e. cross-product

$$(\hat { i } -\hat { j } +\hat { k } )\times (\hat { i } -3\hat { j } -0\hat { k } )$$

 $$\begin{vmatrix} i & j & k \\ 1 & -1 & 1 \\ 1 & -3 & 0 \end{vmatrix}=3\hat { i } -(-1)\hat { j } +(-2)\hat { k } $$

$$=3\hat { i } +\hat { j } -2\hat { k } $$

652524_160827_ans_38112c11d96542739d1ed7def906f1cc.png

Maths

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