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  4. Which of the following is false? 1) If (a, b, c) are direction ratios of a line, then a2+b2+c2 ≠ 1 2) The direction cosines of a line can be its direction ratios but not vice-versa. 3) If (l, m, n) is one set of direction cosines, then (-l,-m,-n) is also a valid set. 4) If (l1, m1, n1) and (l2, m2, n2) are direction cosines of perpendicular lines, then l1 l2+m1 m2+n1 n2=1

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Q. Which of the following is false?
1) If $(a, b, c)$ are direction ratios of a line, then $a^{2}+b^{2}+c^{2} \neq 1$
2) The direction cosines of a line can be its direction ratios but not vice-versa.
3) If $(l, m, n)$ is one set of direction cosines, then $(-l,-m,-n)$ is also a valid set.
4) If $\left(l_{1}, m_{1}, n_{1}\right)$ and $\left(l_{2}, m_{2}, n_{2}\right)$ are direction cosines of perpendicular lines, then $l_{1} l_{2}+m_{1} m_{2}+n_{1} n_{2}=1$

AP EAMCETAP EAMCET 2020

Solution:

If the direction cosines of two perpendicular lines are $l_{1}, m_{1}, n_{1}$ and $l_{2}, m_{2}, n_{2}$, then $l_{1} l_{2}+m_{1} m_{2}+n_{1} n_{2}=0$