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Math 252 Quizzes - Name Math 252:Quiz#1 1 Given the vector...

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Name Math 252:Quiz #1 1) Given the vector v = (2,-5,l) , Normalize the vector. ^ | \7 1 z v C-T) z t- C Q 7 b) Find a vector in the opposite direction of magnitude -v/5 . 2) a) Find the angle between the two vectors u =_(2,-5,7) and v=(0,5,4). -- I tf \lvi cose- ^ '•' v/to* •»-(.-$>*+ <-?> •= TlMTFTi = vT^s, ^ \/3Tis ''" 5"' ( - 2 ~~ ^ b) Find the angle the vector v makes with respect to the X-axis. Hint: Consider (1,0,0) ^ 8 '4. 5" 2 < ^ IV """I y = (2,3) and v - (5,1) Find, -> —> a) The projection of u onto v .(A scalar) b) The component of u onto v ( A vector) —» —> c) The orthogonal component of u with respect to v . V 7 & JJ1N -> r. / ~> c, / /J ' 4) Find the value of the constant k which will make the vectors (2k, 5,0) and (- 1,3,2 perpendicular. Hint: Consider the dot product. C-0 1- Cs)CO t 5) Write the equation of the sphere with center of C(l,4,-3) if the point P(10,4,0) is on the sphere. f Oo^H , o^ of ^ Cx-0't +- o 2 1C,
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Name Math 252 Quiz on Directional Derivatives Suppose you are climbing a hill whose shape is given by z = -2x 2 - 4y 2 +35 You are standing at the point given by (1,1,29) a) How fast is the slope of the surface increasing in the direction of (2 -3 > ?
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