1. Find a vector equation of the line through P(3,-4,-1) parallel to the vector i+j+k. 2. Find a vector equation of the line containing Po(1,2,-1) and P₂(4,3,-2). 3. Find a vector equation of the line that passes through the point P(1,-1,2) and is perpendic- ular to the vectors u=21-3j+k and u=3i+4j+5k. 4. For problems 1-3, find the corresponding parametric equations of the line. 5. For problems 1-3, find the corresponding symmetric equations of the line. 6. Find (1) a point and (2) a vector parallel to the line z(t)=-1+t v(t) =2+4t. z(t) =2+3t 7. Let -4 -2+1 be symmetric equations of a line. Find (1) two point and (2) a -3 vector parallel to the line. (31-3j+k)+(-2j+k) (51-1+k)+1₂(31-6j+3k) 8. Determine whether each pair of lines intersect, are parallel or skew (a) 4 4: - (b) 4 (31-3j+k)+(-2j+k) 4: (51+j+k)+t₂(1-4)+3k) (e) 4 (31+2j+k)+(1-j+k) 4: (51+6)+k)+t₂(1-1)+2k)