Engineering Calculus Notes 82

Engineering Calculus Notes 82 - x − y z = 5 6 Find the...

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70 CHAPTER 1. COORDINATES AND VECTORS (c) 5 x 4 y + z = 8 (d) z = 2 x + 3 y + 1 (e) x = 5 3. Find a parametrization of each plane below: (a) 2 x + 3 y z = 4 (b) z = 4 x + 5 y + 1 (c) x = 5 4. Find an equation for the plane through the point (2 , 1 , 2) (a) parallel to the plane 3 x + 2 y + z = 1 (b) perpendicular to the line given by x = 3 t y = 1 3 t z = 2 t. 5. Find the distance from the point (3 , 2 , 1) to the plane
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Unformatted text preview: x − y + z = 5. 6. Find the angle between P 1 and P 2 : (a) P 1 : 2 x + y − z = 4 P 2 : 2 x − y + 3 z = 3 (b) P 1 : 2 x + 2 y + 2 √ 6 z = 1 P 2 : √ 3 x + √ 3 y + √ 2 z = √ 5 Theory problems: 7. (a) Show: If −→ p ( t ) = −→ p + t −→ v −→ q ( t ) = −→ p + t −→ w...
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