Subjective Type

Find the angle between the lines whose direction ratios are $$a,b,c$$ and $$b-c, c-a, a-b$$

Solution

The angle $$\theta$$ between the lines with direction cosines $$a,b,c$$ and $$b-c, c-a, a-b$$ is given by,
$$\cos

{ \theta } =\left| \cfrac { a(b-c)+b(c-a)+c(a-b) }{ \sqrt { { a }^{ 2 }+{ b

}^{ 2 }+{ c }^{ 2 } } \sqrt { { \left( b-c \right) }^{ 2 }+{ \left(

c-a \right) }^{ 2 }+{ \left( a-b \right) }^{ 2 } } } \right| $$
$$\Rightarrow \cos { \theta } =0$$
$$\Rightarrow \theta=\cos ^{ -1 }{ 0 } $$
$$\Rightarrow \theta ={ 90 }^{ o }$$
Thus, the angle between the lines is $${90}^{o}$$.

SIMILAR QUESTIONS

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