Write the formula for the shortest distance between the lines ` vec r= vec a_1+lambda vec b_1 a n d\ vec r= vec a_2+mu vec b_2dot\ `

Write the condition for the lines vec r= vec a_1+lambda vec b_1 a n d\ vec r= vec a_2+mu vec b_2dot\ to be intersecting.

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

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.

Let A( vec a)a n dB( vec b) be points on two skew lines vec r= vec a+lambda vec pa n d vec r= vec b+u vec q and the shortest distance between the skew lines is 1, w h e r e vec pa n d vec q are unit vectors forming adjacent sides of a parallelogram enclosing an area of 1/2 units. If angle between A B and the line of shortest distance is 60^0, then A B= a. 1/2 b. 2 c. 1 d. lambda R={10}

Let A( vec a)a n dB( vec b) be points on two skew lines vec r= vec a+lambda vec pa n d vec r= vec b+u vec q and the shortest distance between the skew lines is 1, w h e r e vec pa n d vec q are unit vectors forming adjacent sides of a parallelogram enclosing an area of 1/2 units. If angle between A B and the line of shortest distance is 60^0, then A B= a. 1/2 b. 2 c. 1 d. lambda R={0}

Statement 1: Lines 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) intersect. Statement 2: vec bxx vec d=0 , then lines vec r= vec a+lambda vec ba n d vec r= vec c+lambda vec d do not intersect.

Write the equation of the plane vec r= vec a+lambda vec b+mu vec c\ in scalar product form.

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

For any vector vec a\ a n d\ vec b prove that | vec a+ vec b|lt=| vec a|+| vec b|dot

Find | vec a- vec b|,\ if:| vec a|=3,\ | vec b|=4\ a n d\ vec adot vec b=1