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Unformatted text preview: m 1.6 on p. 8).
5. Find the equation of a line passing through points (0,2,0) and (1,0,0), in the vector
form, r = a + λ b , where λ is any real number (a parameter). Make a sketch. Check
that it agrees with the slope-intercept equation of this line in a plane (y = a x + b).
6. Draw vectors a and b that satisfy the condition | a - b |2 = | a |2 + | b |2
7. Expand the following expressions (use the distributive property and other properties
of the dot and cross vector products); simplify if possible:
a) | a × b |2 + ( a · b )2
b) ( a + b ) × ( a − b )
c) ( a + b ) · ( a − b )
8. Find the equation of the plane that is perpendicular to the vector (1,-1,3) and passes
through the point (1, 0, 2) (Review your Calculus III material)...
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