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scan0093

# scan0093 - f what is the equation for the plane containing...

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Unformatted text preview: f. what is the equation for the plane containing 17 and iv The perpendicular vector, also known as the normal vector is given byii x W2— 14? +4j'+ 56/; and a point in the plane is (0,0,0)so using the equation on page 79 a(x — x0) + My — yo) + c(z — 20) = OWhere (a,b,c) is the normal vector therefore the equation of the plane is is given by : — l4x+4y+ 562 = 0 g. What is the magnitude of vector 17 in the direction of ii : 07+9f+3l§ 0i+3f+l§ unit vector in direction u 2% = V02 + 92 + 32 V10 the magnitude of v in the direction of u is therefore: q Oi+3f+l€ 8?+0~'+21; Oi+3f+l§ 2 v0“: 1 O“:— M j 45 J16 Problem4 (25pts.) a. Find all the critical points of the function: 5 5 fCXJJ/F xy+7+7 x y . 10 10 30 x, = —— =x_— x: =+_ fx( y) y x3 fy y3 fxx( 3/) x4 critical points occur when 3 and 13, are equal to zero: 10 10 x, = —— : 0 = x——— : fx( 3’) y x3 fy 373 therefore 10 10 y=—3 and x:— 30 fyy<x=y) = F fxy(x,y) = 1 ...
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