Show that the straight lines whose direction cosines are given by the equations `a l+b m+c n=0a n dul^2+z m^2=v n^2+w n^2=0` are parallel or perpendicular as `(a^2)/u+(b^2)/v+(c^2)/w=0ora^2(v+w)+b^2(w+u)+c^2(u+v)=0.`

Show that the straight lines whose direction cosines are given by the equations al+bm+cn=0 and ul^(2)+zm^(2)=vm^(2)+wn^(2)=0 are parallel or perpendicular as (a^(2))/(u)+(b^(2))/(v)+(c^(2))/(w)=0 or a^(2)(v+w)+b^(2)(w+u)+c^(2)(u+v)=0

The angle between the straight lines, whose direction cosines are given by the equations 2l+2m -n=0 and mn+nl+lm=0 , is :

The angle between the lines whose direction cosines are given by the equatios l^2+m^2-n^2=0, m+n+l=0 is

Find the angle between the lines whose direction cosine are given by the equation: "l"-"m"+"n"=0" and l"^2-"m"^2-"n"^2=0

If the roots of the equation x^(3) -10 x + 11 = 0 are u, v, and w, then the value of 3 cosec^(2) (tan^(-1) u + tan^(-1) v + tan^(-1 w) is ____

Let vec u,vec v and vec w be such that |vec u|=1,|vec v|=2 and |vec w|=3. If the projection of vec v along vec u is equal to that of vec w along vec u and vectors vec v and vec w are perpendicular to each other,then |vec u-vec v+vec w| equals 2 b.sqrt(7)c.sqrt(14)d.14