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

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. (1,3,4) c. (-1,3,4) d. none of these

If vec a\ a n d\ vec b are unit vectorts, then the greatest value fo sqrt(3)| vec a+ vec b|+| vec a- vec b| is (a).2 (b). 2sqrt(2) (c).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

Find the value of lambda so that the following vectorts are coplanar: vec a= hat i+3hat j,\ vec b=5 hat k ,\ vec c=lambda hat i- hat j

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

Write the equation of the plane containing the lines vec r= vec a+lambda vec b\ a n d\ vec r= vec a+mu vec c

The value of [ vec a- vec b ,\ vec b- vec c ,\ vec c- vec a],\ w h e r e\ | vec a|=1,\ | vec b|=5,\ | vec c|=3, i s 0 b. "1 c. 6 d. none of these

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

Write the position vector of the point where the line vec r= vec a+lambda vec b meets the plane vec r dot (vec n)=0.

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