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prove that the lines whose direction cosines are given by ul^2+vm^2 wn^2=0 and al+bm+cn=0 are (i) perpendicular if u(b^2+c^2)+v(C^2+a^2)+w(a^2+b^2)=0 (ii) parallel if a^2/u + b^2/v + c^2/w =0. prove that the lines whose direction cosines are given by ul^2+vm^2 wn^2=0 and al+bm+cn=0 are (i) perpendicular if u(b^2+c^2)+v(C^2+a^2)+w(a^2+b^2)=0 (ii) parallel if a^2/u + b^2/v + c^2/w =0.
prove that the lines whose direction cosines are given by
ul^2+vm^2 wn^2=0 and al+bm+cn=0 are
(i) perpendicular if u(b^2+c^2)+v(C^2+a^2)+w(a^2+b^2)=0
(ii) parallel if a^2/u + b^2/v + c^2/w =0.
Dear student, u1 = [l1, m1, n1] is a unit vector along one line u2 = [l2, m2, n2] is a unit vector along the other line The cross product, u1 x u2 is perpendicular to both and is a unit vector. Its components are [m1n2 − m2n1, n1l2 − n2l1, l1m2 − l2m1]
Dear student,
u1 = [l1, m1, n1] is a unit vector along one line u2 = [l2, m2, n2] is a unit vector along the other line The cross product, u1 x u2 is perpendicular to both and is a unit vector. Its components are [m1n2 − m2n1, n1l2 − n2l1, l1m2 − l2m1]
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