Find the acute angle between the following lines.
`(x+4)/(3)=(y-7)/(4)=(z+5)/(5),vec(r)=4hat(k)+t(2hat(i)+hat(j)+hat(k))`

Find the acute angle between the following lines. vec(r)=(4hat(i)-hat(j))+t(hat(i)+2hat(j)-2hat(k)) vec(r)=(hat(i)-2hat(j)+4hat(k))+s(-hat(i)-2hat(j)+2hat(k))

Find the angel between the following pair of lines: vec r=2 hat i-5 hat j+ hat k+lambda(3 hat i+2 hat j+6 hat k)a n d vec r=7 hat i-6 hat k+mu( hat i+2 hat j+2 hat k) x/2=y/2=z/1a n d(x-5)/4=(y-2)/1=(z-3)/8

Find the angle between the line vec(r)=(2hat(i)-hat(j)+hat(k))+t(6hat(i)+2hat(j)-2hat(k))" and the plane "vec(r)*(6hat(i)+3hat(j)+2hat(k))=8

Find the angle between the planes vec(r)*(hat(i)+hat(j)-2hat(k))=3and2x-2y+z=2

Find the parametric form of vector equation, and Cartesian equations of the plane containing the line vec(r)=(hat(i)-hat(j)+3hat(k))+t(2hat(i)-hat(j)+4hat(k))" and perpendicular to plane "vec(r)*(hat(i)+2hat(j)+hat(k))=8.

The angle between the lines vec(r)=(hat(i)+2hat(j)-3hat(k))+t(2hat(i)+hat(j)-2hat(k))" and the plane "vec(r)*(hat(i)+hat(j))+4=0 is

Find the shortest distance between the lines whose vector equations are vec r=(4 hat i- hat j)+ lambda(hat i+2 hat j-3 hat k) and vec r=(hat i - hat j+2 hat k)+mu(hat i +4 hat j-5 hat k)

Find the parametric form of vector eqution of the straight line passing through (-1,2,1) and paralle to the straight line vec(r)=(2hat(i)+3hat(j)-hat(k))+t(hat(i)-2hat(j)+hat(k)) and lines find the shortest distance between the lines.

Represent the following vectors graphically : vec(A) = 3 hat(i) + 4 hat(j), vec(B) = 2 hat(i) - 3 hat(j) : vec(C) = - 5 hat(i) - 4 hat(j) : vec(D) = - 4 hat(i) + 3 hat(j)

Represent the following vectors graphically : vec(A) = 3 hat(i) + 4 hat(j), vec(B) = 2 hat(i) - 3 hat(j) : vec(C) = - 5 hat(i) - 4 hat(j) : vec(D) = - 4 hat(i) + 3 hat(j)