sider the 3-dimensional coordinate system pictured below. Suppose u is a vector

Question

sider the 3-dimensional coordinate system pictured below. Suppose u is a vector extending n the rz-plane whose coordinate in the the z and z positions are negative. Additionally suppose v is a vector extending in the -plane whose coordinate in the the z position is positive, and whose coordinate in the z position is negative. Which description below describes the direction of u x v? (a) Parallels the r-axis and points in the negative direction. (b) Parallels the s-axis and points in the positive direction. (c) Parallels the y-axis and points in the negative direction (d) Parallels the y-axis and points in the positive direction. 8. Find the area of the parallelogram whose four vertices are at the points P-(,-1,2) Q = (3. 1.5). R-u 2.7), and s-(2.0.4) (a) (b) 12 (c) VTT (d)v2 9. Find parametric equations for the line that passes through the point P = (-2, 1,-3) and is parallel to the vector u = 3i + -2k.

Explanation / Answer

9. The equation of line in parametric form is given by:

x-x0 / a = y -y0/ b = z - z0/ c

(x0, y0, z0) --> point on line

(a,b,c) --> direction vector of line

(x0, y0, z0) --> (-2, 1, -3)

Since line l parallel to given vector, hence line l has same direction vectors

(a, b,c) --> (3, 2, -2)

Parametric equation of line:

x = -2 + 3t

y = 1 + 2t

z = -3 -2t

option (c) is correct.

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