[" Cartesian form of the equation of line "bar(r)],[bar(3)j-5j+7bar(k)+lambda(2i+j-3bar(k))is]

The shortest distance the two lines bar(r)=2bar(i)-bar(j)-bar(k)+lambda(2bar(i)+bar(j)+2bar(k)) and bar(r)=(bar(i)+2bar(j)+bar(k))+mu(bar(i)-bar(j)+bar(k)) is

The shortest distance between the lines bar(r)=3bar(i)+5bar(j)+7bar(k)+lambda(bar(i)+2bar(j)+bar(k)) and bar(r)=-bar(i)-bar(j)+bar(k)+mu(7bar(i)-6bar(j)+bar(k)) is

The position vector of the foot of theperpendicular from (1,-2,-3) to the line bar(r)=bar(i)+bar(j)+lambda(2bar(i)+bar(j)+bar(k)) is

The vector equation of the line joining the points 3bar(i)+2bar(j)-4bar(k), 5bar(i)+4bar(j)-6bar(k) is

Cartesian equation of the line passing through the points bar(a)=2bar(i)+bar(j)-2bar(k) and bar(b)=2bar(i)+2bar(j)-bar(k) is

Find the vector area and area of the triangle with vertices bar(i) + bar(j)-bar(k), 2bar(i)- 3bar(j) + bar(k), 3 bar(i) + bar(j)- 2bar(k) .

The position vectors of the vertices of a triangle are 3bar(i)+4bar(j)+5bar(k),bar(i)+7bar(k) and 5bar(i)+5bar(j) The distance between the circumcentre and orthocentre is

Find the vector equation of the plane passing through the points bar(i)-2bar(j)+5bar(k), -5bar(j)-bar(k), -3bar(i)+5bar(j) .

Find the vector equation of the line passing through the points -2bar(i)+3bar(j)+5bar(k), bar(i)+2bar(j)+3bar(k) .

If the triangle formed by the vectors 3 bar(i) + 5 bar(j) + 2 bar(k) , 2 bar(i) - 3 bar(j) - 5 bar(k) and - 5 bar(i) - 2 bar(j) + 3 bar(k) equilateral ?