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.

Question

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.

SAGAR SINGH - IIT DELHI · Answer

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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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.

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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.

1 Answers

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

Other Related Questions on Magical Mathematics[Interesting Approach]

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a Complete All-in-One Study package Fully Loaded inside a Tablet!

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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.