HW (due this Friday) 1.2: 25, 26, 29, 34, 36, 38; 1.3: 8, 10, 14, 17, 20, 25, 28; 1.4: 4, 10, 12, 13, 17, 19, 25; 1.5: 3, 8, 9, 15, 20

Find an equation of the line containing the point p and is parallel to the vector a

Find an equation of the plane containing the point p and containing the vectors a and b

Find the equation of the plane containing the points (1, 2, 3), (5, 4, 7), (0, 0, 6).

Normal form:

Find the equation of the plane containing the point p and orthogonal to the vector n

Find the equation of the plane containing the points (1, 2, 3), (5, 4, 7), (0, 0, 6). n · [(x − p)] = 0 (n_{1}, n_{2}, n_{3}) · [(x_{1}, x_{2}, x_{3}) − (p_{1}, p_{2}, p_{3})] = 0 (n_{1}, n_{2}, n_{3}) · (x_{1} − p_{1}, x_{2} − p_{2}, x_{3} − p_{3}) = 0 n_{1}(x_{1} − p_{1}) + n_{2}(x_{2} − p_{2}) + n_{3}(x_{3} − p_{3}) = 0 n_{1}x_{1} + n_{2}x_{2} + n_{3}x_{3} = n_{1}p_{1} + n_{2}p_{2} + n_{3}p_{3} Equation of a plane in R^{3} in normal form:

Ax + By + Cz = D

Equation of plane in other form x = sa + tb + p Find the intersection of the planes x−2y +5z = 0 and 3x + 4y = 0

Find the distance between the point (1, 2, 3) and the line x = t(4, 2, 5) + (0, 6, 2)