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Unformatted text preview: MATH 265: MULTIVARIABLE CALCULUS: LESSON 1 PROBLEMS (1) Upload the pdf ﬁle with the solutions to these problems to Blackboard for grading. Be sure to show all the steps necessary for the solution. The work must be organized so that I can follow your steps. (2) In this and all future assignments, always give answers in exact form if possible. Decimal approximations are used only when there is no √ choice. For example, if an answer to a problem works out to 2π , leave that answer in that form. Do not use a calculator to ﬁnd the decimal approximation 4.442882938. (3) Be sure to use correct notation for vectors. That means enclosing vector components in brackets ( a, b, c ) and writing arrows above symbols → representing vectors (− ). v (4) Be sure to remember items (1), (2), and (3) for all future assignments! Problems are worth 20 points each. → → (1) Let − = 3, −1 , and − = 1, 2 . v w →→→ → →→ (a) Sketch the vectors − , − , − − − , and 2− + − . vwv w v w −. → (b) Find a unit vector in the direction of v − − → (2) Let P = (2, 4), Q = (−1, 3), R = (3, 8), S = (−6, 6). Determine if the vectors P Q − → and RS are parallel. (3) A line in space passes through the points P = (4, 0, 1) and Q = (−2, 3, 5). (a) Write down a vector parametrization for the line. (b) Write down parametric equations for the line. (See the box, top of page 672.) (4) Find an equation for the line through the point P = (1, 0, −3) and perpendicular to the xy plane. → → (5) Determine if the lines −1 (t) = 3, 0, 2 + t 1, 2, −2 and −2 (s) = 0, 1, −1 + s 4, 1, 1 r r intersect, and if they do, ﬁnd the point of intersection. (6) (Bonus question: worth 10 points. Total points for assignment not to exceed 100.) Suppose a, b are two positive numbers. Find an equation for the line in space passing through a on the xaxis and b on the y axis.
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This note was uploaded on 02/24/2011 for the course MATH 265 taught by Professor Jerrymetzger during the Winter '11 term at North Dakota.
 Winter '11
 JerryMetzger
 Calculus, Multivariable Calculus

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