Value of `lambda` such that the line `(x-1)/2=(y-1)/3=(z-1)/lambda` is `_|_` to normal to the plane ` vec r.(2 vec i+3 vec j+4 vec k)=0` is a. `-(13)/4` b. `-(17)/4` c. `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 sin theta=1//3, the value of lambda is a. -3/5 b. 5/3 c. -4/3 d. 3/4

The centre of the circle given by vec r.( 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. (1,3,4) c. (-1,3,4) 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 (-3)/4 b. 1/4 c. 3/4 d. 1/2

The vector equation of the plane passing through the origin and the line of intersection of the planes vec r. vec a = lambda and vec r. vec b =mu is __

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 k and 3 vec i-5 vec j+8 vec k is a. 1:5 b. 1: 10 c. 3:5 d. 3: 10

The volume of he parallelepiped whose sides are given by vec O A=2i-2j , vec O B=i+j-k a n d vec O C=3i-k is a. 4/13 b. 4 c. 2/7 d. 2

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

Find the angle between the lines vec r= dot( hat i+2 hat j- hat k)+lambda( hat i- hat j+ hat k) and the plane vec r . dot(3 hat i- hat j+ hat k)=4.

The distance between the line vec r=(2 hat i-2 hat j+3 hat k)+lambda( hat i- hat j+4 hat k) and plane vec rdot(( hat i+5 hat j+ hat k))=5.

Statement 1: Line (x-1)/1=(y-0)/2=(z+2)/(-1) lies in the plane 2x-3y-4z-10=0. Statement 2: if line vec r= vec a+lambda vec b lies in the plane vec r. vec c=n (where n is scalar),then vec b. vec c=0. (a) Both the statements are true, and Statement 2 is the correct explanation for Statement 1. (b) Both the Statements are true, but Statement 2 is not the correct explanation for Statement 1. (c)Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true.