(a) Find the points where the curve r = t i + t 2 j − 3 t k intersects the plane 2 x − y + z = − 2. (b) For the curve and plane in part (a), find, to the nearest degree, the acute angle that the tangent line to the curve makes with a line normal to the plane at each point of intersection.
(a) Find the points where the curve r = t i + t 2 j − 3 t k intersects the plane 2 x − y + z = − 2. (b) For the curve and plane in part (a), find, to the nearest degree, the acute angle that the tangent line to the curve makes with a line normal to the plane at each point of intersection.
(a) Find the points where the curve
r
=
t
i
+
t
2
j
−
3
t
k
intersects the plane
2
x
−
y
+
z
=
−
2.
(b) For the curve and plane in part (a), find, to the nearest degree, the acute angle that the tangent line to the curve makes with a line normal to the plane at each point of intersection.
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