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# exercises4 - are perpendicular 7 Find the vector projection...

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EXERCISES – 4 1) Find an equation for the plane through the points (3,2,-1) , (1,-1,3) and (3,-2,4). 2) Find the acute and obtuse angles between the planes 4x + 4y - 2z = 9 and 2x + y + z = -3. 3) Find an equation of the plane containing t he point P(1,3,1) and the line L given by the parametric equations x = t, y = t, z = t + 2 . 4) Show that 0 Ax A = ca ca a for any vector A ca in 3 R . 5) Show that the line 3 1 4 5 5 7 x y z - + + = = lies in the plane 3x + 4y - 5z = 25 6) Find the value of k for which the planes 3x – 4y + 2z + 9 = 0 and 3x + 4y – kz + 7 = 0
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Unformatted text preview: are perpendicular. 7) Find the vector projection of 1,2,4 u =< > a on 4, 2,4 v =<-> a . 8) Show that ( ) [( ) ( )] 2 ( ) A B B C A C A B C + • + × + = • + ca ca ca ca ca ca ca ca ca . 9) Find the distance beween the lines 2 3 1 2 3 & 2 2 4 3 5 x z x y z y +- -+- +-= - + = = = 10) Find an equation of the sphere with center at (1,2,3) and tangent to the yz-plane....
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