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For what value of c the vector 2 straight i with hat on top plus straight c straight j with hat on top will be perpendicular to:
(i) Z-axis      (ii) Y-axis?


(i) Vector 2 straight i with hat on top plus straight c straight j with hat on top is perpendicular to Z-axis if its dot product with <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
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#6 {main}</pre> is zero.

i.e.                       left parenthesis 2 straight i with hat on top plus straight c straight j with hat on top right parenthesis times straight k with hat on top equals 0

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#6 {main}</pre>

rightwards double arrow                      2 left parenthesis 0 right parenthesis plus straight c left parenthesis 0 right parenthesis space equals space 0

The equation is satisfied for all values of c.

Therefore left parenthesis 2 straight i with hat on top plus straight c straight j with hat on top right parenthesis is always perpendicular to Z-axis whatever the value of c.

(ii) Similarly        left parenthesis 2 straight i with hat on top plus straight c straight j with hat on top right parenthesis times straight j with hat on top equals 0

rightwards double arrow                    2 straight i with hat on top. straight j with hat on top plus straight c space straight j with hat on top. space straight j with hat on top space equals space 0

rightwards double arrow                            space space 0 plus straight c space equals space 0

rightwards double arrow                                    straight c equals 0

∴  left parenthesis 2 straight i with hat on top plus straight c straight j with hat on top right parenthesis is perpendicular to Y-axis if c = 0.

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