Unformatted text preview: he plane. But
4 Here
−
−
→
P Q = −3, 4, 0 , −
→
P R = −3, 0, 2 . =4 2 −3 3 −3 −4 3 2 −3 2 a · ( b × c) = −1
3 −3 + 3 −3 2 −3 −4 32
23 . geyer (dag2798) – HW09 – rusin – (55735) 4 Consequently,
keywords: line, parametric equations, direction vector, point on line, intercept, coordinate plane volume = 11 . keywords: determinant, cross product, vector
product, scalar triple product, parallelopiped,
volume,
007 008 10.0 points Find parametric equations for the line
passing through the points P (4, 1, 2) and
Q(5, 5, 5). 10.0 points A line ℓ passes through the point P (1, 4, 4)
and is parallel to the vector 2, 3, 4 .
At what point Q does ℓ intersect the xy plane? 1. x = 4 + t,
correct y = 1 + 4t, z = 2 + 3t 2. x = 4 − t, y = 1 + 4t, z = 2 − 3t
3. x = 1 + 4t, y = 4 − t, z = 3 + 2t 1. Q(1, −1, 0) 4. x = 1 + 4t, y = 4 + t, z = 3 + 2t 2. Q(0, −1, 7) 5. x = 1 − 4t, y = 4 + t, z = 3 − 2t 3. Q(−1, 1, 0) correct 6. x = 4 + t, y = 1 − 4t, z = 2 + 3t 4. Q(0, 7, 3) Explanation:
A line passing through a point P (a, b, c)
and having direction vector v is given parametrically by 5. Q(0, 3, 1)
6. Q(3, 7, 0)
Explanation:
Since the xy plane is given by z = 0, we
have to ﬁnd an equation for ℓ and then set
z = 0.
Now a line passing through a point
P (a, b, c) and ha...
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This note was uploaded on 05/12/2013 for the course M 408d taught by Professor Sadler during the Spring '07 term at University of Texas.
 Spring '07
 Sadler
 Determinant, Multivariable Calculus

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