A point on the line `r=(1-t)(2i +3j +4k) +t(3i -2j+2k)` is​

A point on the line bar(r)=(1-t)(2bar(i)+3bar(j)+4bar(k))+t(3bar(i)-2bar(j)+2bar(k))

If theta is the between the line r = ( i + 2j- k) + lambda (i - j + 2k) , lambda in R and the plane r. (2i - j + k ) = 4. then a value of cos theta is :

A point on the line r=2vec i+3vec j+4vec k+t(vec i+vec j+vec k) is

If the points with position vectors -i + 3j + 2k , -4i + 2j - 2k and 5i + lamda j + μk lie on a straight line in space, then

A point on the line hat r=2hat i+3hat j+4hat k+t(hat i+hat j+hat k) is

A point on the line vec r=2hat i+3hat j+4hat k+t(hat i+hat j+hat k) is

The shortest distance between the lines r=(4i-j)+lambda(i+2j-3k) and r=(i-j+2k)+mu(2i+4j-5k) is

Line of intersection of the two planes barr.(3i - j + k)=1 and barr.(i+4j-2k)=2 is parallel to the vector