The length of altitude through the vertex A of triangle ABC,The position vectors of whose vertices are `bar(a),bar(b),bar(c)`

Prove that the area of the triangle,whose positionvectors of vertices are bar(a),bar(b),bar(b),bar(b), will be (1)/(2)|bar(b)xxbar(c)+bar(c)xxbar(a)+bar(a)xxbar(b)|

In a triangle ABC ,right angled at the vertex A ,if the position vectors of A, B and C are respectively 3bar(i)+bar(j)-bar(k), -bar(i)+3bar(j)+pbar(k) and 5bar(i)+qbar(j)-4bar(k), then the points (p,q) lies on a line

If bar(a),bar(b),bar(c) are non-coplanar unit vectors each including the angle of measure 30^(@) with the other, then find the volume of tetrahedron whose co-terminal edges are bar(a),bar(b),bar(c) .

Let M be the foot of the altitude drawn from the vertex B to side AC of Delta ABC whose vertices are A(1,-2,2)B(1,4,0)C(-4,1,1) then bar(BM)=

Let ABC be a triangle whose circumcentre is at P. If the position vectors of A,B,C and P are bar(a),bar(b),bar(c) and (bar(a)+bar(b)+bar(c))/(4) respectively then the positive vector of the orthocentre of the triangle is

If bar(a) is the position vector of A then the position vector of the foot of the perpendicular from A to the plane bar(r).bar(b)=bar(b).bar(c) is.

Derive the expression for the volume of the prallelopiped whose coterminus edges are vectors bar(a),bar(b),bar(c) .

If bar(a),bar(b),bar(c) are position vectors of vertices A,B,C of Delta ABC. If bar(r) is position vector of apoint P such that (|bar(b)-bar(c)|+|bar(c)-bar(a)|+|bar(a)-bar(b)|)bar(r)=|bar(b)-bar(c)|bar(a)+|bar(c)-bar(a)|bar(b)+|bar(a)-bar(b)|bar(c) then the point P is

If line joining points A and B having position vectors 6bar(a)-4bar(b)+4bar(c) and -4bar(c) respectively, and the line joining the points C and D having position vectors -bar(a)-2bar(b)-3bar(c) and bar(a)+2bar(b)-5bar(c) intersect,then their point of intersection is (A) B(B)C(C)D(D)A

If bar(b),bar(c) are two unit vectors along the positive x,y axes,and bar(a) is any vector,then (bar(a)*bar(b))bar(b)+(bar(a)*bar(c))bar(c)+(bar(a)*(bar(b)xxbar(c)))/(|bar(b)xxbar(c)|)(bar(b)xxbar(c))=