Value of `lambda` such that the line `(x-1)/2=(y-1)/3=(z-1)/lambda` is `_|_` to normal to the plane ` vec rdot(2 vec i+3 vec j+4 vec k)=0` is a. `-(13)/4` b. `-(17)/4` c. `4` d. none of these

Find the angle between the line vec r=( vec i+2 vec j- vec k)+lambda( vec i- vec j+ vec k) and the normal to the plane vec rdot((2 vec i- vec j+ vec k))=4.

The centre of the circle given by vec rdot( hat i+2 hat j+2 hat k)=15a n d| vec r-( hat j+2 hat k)|=4 is a. (0,1,2) b. (1,3,5) c. (-1,3,4) d. none of these

If angle theta bertween the line (x+1)/1=(y-1)/2=(z-2)/2 and the plane 2x-y+sqrt(lambda)z+4=0 is such that s intheta=1//3, the value of lambda is a. -3/5 b. 5/3 c. -4/3 d. 3/4

The angle between i+j line of the intersection of the plane vec rdot( hat i+2 hat j+3 hat k)=0a n d vec rdot(3 hat i+3 hat j+ hat k)=0 is a. cos^(-1)(1/3) b. c0s^(-1)(1/(sqrt(3))) c. cos^(-1)(2/(sqrt(3))) d. none of these

If vec aa n d vec b are two unit vectors incline at angle pi//3 , then { vec axx( vec b+ vec axx vec b)}dot vec b is equal to a. (-3)/4 b. 1/4 c. 3/4 d. 1/2

Show that the vector veci -2 vec j +3 vec k , -2 vec i + 3 vecj -4 vec k " and " -vec j + 2 vec k are coplanar.

Show that the vector veci -2 vec j +3 vec k , -2 vec i + 3 vecj -4 vec k " and " -vec j + 2 vec k are coplanar.

Find the angle between the line vec r= hat i+2 hat j- hat k+lambda( hat i- hat j+ hat k) and the plane vec rdot(2 hat i- hat j+ hat k)=4.

The vector equation of the plane passing through the origin and the line of intersection of the planes vec rdot vec a=lambdaa n d vec rdot vec b=mu is a. vec rdot(lambda vec a-mu vec b)=0 b. vec rdot(lambda vec b-mu vec a)=0 c. vec rdot(lambda vec a+mu vec b)=0 d. vec rdot(lambda vec b+mu vec a)=0

The ratio in which the plane vec rdot( vec i-2 vec j+3 vec k)=17 divides the line joining the points -2 vec i+4 vec j+7 vec ka n d3 vec i-5 vec j+8 vec k is a. 1:5 b. 1: 10 c. 3:5 d. 3: 10