If vector r wiith dc's l,m,n is equally inclined to the coordinate axes, then the total number of such vectors is
If a,b and c are three mutually perpendicular vectors, then the projection of the vectors l(a)/(|a|)+m(b)/(|b|)+n((axxb))/(|axxb|) along the angle bisector of the vectors a and b is
If l_(1),m_(1),n_(1) and l_(2),m_(2),n_(2) are the directional cosines of two vectors and theta is the angle between them, then their value of cos theta is
Redox Reactions L2
Let L_1, L_2, L_3 be three distinct lines in a plane P and another line L, is equally inclined with these three lines. Statement-1: The line L is normal to the plane P. because Statement-2: if non zero vector vec V is equally inclined to three non zero coplanar vector vec V_1, vec V_2, vec V_3 then the vector vec V is normal to the plane of vec V_1, vec V_2 and vec V_3
If l,m,n are the d.c's of a vector if l=(1)/(2) then maximum value of lmn=
bara and barb are two non-collinear vectors that the points with position vectors l_1bara+m_1bar,l_2bara+m_2barb,l_2bara=m_3 barb . Are collinear then find the value of |:(1,1,1),(l_1,l_2,l_3),(m_1,m_2,m_3):|
vec a and vec b are two non-collinear vectors. Show that the points with position vectors l_(1)vec a+m_(1)vec b,l_(2)vec a+m_(2)vec b,l_(3)vec b are collinear if l_(1)quad l_(2)quad l_(3)m_(1)quad m_(2)quad m_(3)]|=0
Line L_(1) is parallel to vector vec(alpha) = - 3hati + 2hatj+ 4hatk and passes through a point A(7, 6, 2) and line L_(2) is parallel to a vector vec(beta) = 2hati + 2hatj + 3hatk and passes through a point B(5,3,4). Now a line L_(3) parallel to a vector vec(r) = 2hati - 2hatj - hatk intersects the line L_(1) and L_(2) at point C and D respectively, Find |vec(CD)| .
Consider the lines L_1 : r=a+lambdab and L_2 : r=b+mua , where a and b are non zero and non collinear vectors. Statement-I L_1 and L_2 are coplanar and the plane containing these lines passes through origin. Statement-II (a-b)cdot(atimesb)=0 and the plane containing L_1 and L_2 is [r a b]=0 which passe through origin.
