Which of the following lines lie on the plane `x+2y-z+4=0?` a. `(x-1)/1=y/(-1)=(z-5)/1` b. `x-y+z=2x+y-z=0` c. ` hat r=2 hat i- hat j+4 hat k+lambda(3 hat i+ hat j+5 hat k)` d. none of these

Find the equation of the plane through the pooint (4,-3,2) and perpendicular to the line of intersection of the planes x-y+2z-3=0 and 2z-y-3z=0 FInd the point of the intersection of the line vec r=hat i+2hat j-hat k+lambda(hat i+3hat j-9hat k) and the plane obtained above

If vec r=x hat i+y hat j+z hat k ,\ then write the value of | vec rxx hat i|^2dot

Find the image of the point (1,6,3) in the line (x)/(1)=(y-1)/(2)=(z-2)/(3). Find the shortest distance between the lines; vec r=(4hat i-hat j)+lambda(hat i+2hat j-3hat k)

The unit vector orthogonal to vector hat i+hat j+2hat k and making equal angles with the x and y -axis a.t (1)/(3)(2hat i+2hat j-hat k) b.+-(1)/(3)(hat i+hat j-hat k) c.+-(1)/(3)(2hat i-2hat j-hat k) d. none of these

Find the distance between points of intersection of and Lines (x-1)/(2)=(y-2)/(3)=(z-3)/(4)(x-4)/(5)=(y-1)/(2)=z and lines vec r=(hat i+hat j-hat k)+lambda(3hat i-hat j)&vec r=(4hat i-hat k)+mu(2hat i+3hat k)

Determine whether the following pair of lines intersect or not. (1) vec r= hat i-5 hat j+lambda(2 hat i+ hat k); vec r=2 hat i- hat j+mu( hat i+ hat j- hat k) (2) vec r= hat i+ hat j- hat k+lambda(3 hat i- hat j); vec r=4 hat i- hat k+mu(2 hat i+3 hat k)

By computing the shortest distance determine whether the following pairs of lines intersect or not: vec r=( hat i- hat j)+lambda(2 hat i+ hat k)a n d vec r=(2 hat i- hat j)+mu( hat i+ hat j- hat k) vec r=( hat i+ hat j- hat k)+lambda(3 hat i- hat j)a n d vec r=(4 hat i- hat k)+mu(2 hat i+3 hat k) . (x-1)/2=(y+1)/3=za n d(x+1)/5=(y-2)/1; z=2 (x-5)/4=(y-7)/(-5)=(z+3)/(-5)a n d(x-8)/7=(y-7)/1=(z-5)/3 .

If the z -intercept of the plane which is passing through the intersection of the planes x+2y+3z+5=0 and 2x-5y+4z+7=0 and parallel to the line vec r=2hat i+5hat j+hat k+t(hat i+hat j+2hat k) is lambda then [|lambda|] equals (where t in R ) (where [.] denotes greatest integer function)

Find the distance of the point (-1,-5,-10) from the point of intersection of the line vec r=2hat i-hat j+2hat k+lambda(3hat i+4hat j+2hat k) and the plane vec r*(hat i-hat j+hat k)=5

Find the angle between the line -> r=(2 hat i+3 hat j+9 hat k)+lambda(2 hat i+3 hat j+4 hat k) and the plane -> r(dot( hat i+ hat j+ hat k))=5.