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

Question

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 (A) 1 (B) 2 (C) 3 (D) 4

Tardigrade Admin · Accepted Answer

If the direction cosines of two perpendicular lines are l1, m1, n1 and l2, m2, n2, then l1 l2+m1 m2+n1 n2=0

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If the direction cosines of two perpendicular lines are l1​,m1​,n1​ and l2​,m2​,n2​, then l1​l2​+m1​m2​+n1​n2​=0

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