Question

Find the value of c if a is a unit vector 2i+cj-9k

Answer 1

$\Huge{\underline{\underline{\mathfrak{Correct \ Question \colon}}}}$

Find the value of 'c' from the following,if a is an unit vector

$\large{ \sf{a = 2 \hat{i} + c \hat{j} - 9 \hat{k}}}$

$\Huge{\underline{\underline{\mathfrak{Answer \colon}}}}$

Given that a is an unit vector » It has an magnitude 1

$\implies \: \sf{1 = \sqrt{2 {}^{2} + c {}^{2} + ( - 9) {}^{2} } }$

Squaring on both sides,we get :

$\implies \: \sf{1 = c {}^{2} + 4 + 81 } \\ \\ \implies \: \sf{c {}^{2} + 85 = 1 } \\ \\ \implies \: \sf{c {}^{2} = - 84} \\ \\ \implies \: \sf{c = \sqrt{- 84} } \\ \\ \implies \boxed{\boxed{\sf{c = 2 \sqrt{21} \iota \ units}}}$

Answer 2

Question :-

$\sf{\red{find \: the \: value \: of \: c \: if \: it \: is \: }}\\ \sf{\green{a \: unit \: vector} }\\ \sf{ a \: =\blue{ 2 \hat{i} + c \hat{j} - 9 \hat{k}}}$

Answer :-

$\rightarrow \: \boxed{\sf{ c \: = \red{\sqrt{ - 84} }} }\:$

To find :-

→ Value of "c",

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Formula used :-

$\sf{ \red{if \: a \:} = \green{x \hat{i} + y \hat{j} \: + z \hat{k}}} \: \: \: \: .......(1)\\ \\ \sf{|a| \: = \blue{ \sqrt{ {x}^{2} + {y}^{2} + {z}^{2} } } }$

Solution :-

Given that, it is unit vector therefore its magnitude is 1.

Hence,

$\sf{\red{comparing \: between \: the\: given \:} } \\ \sf{ \green{vector \: and \: eq(1)}}\\ \\ \sf{ we \: get \: } \\ \rightarrow \sf{x \: = 2 \:, \: y = c \: , \: z = - 9} \\ \\ \implies \sf{ \red{1 = } \green{\sqrt{ {(2)}^{2} + {(c)}^{2} + {( - 9)}^{2} }}} \: \\ \\ \implies \sf{ 1 = \red{\sqrt{4 + 81 + {c}^{2} } } }\\ \\ \implies \sf{1 = \blue{\sqrt{85 + {c}^{2} } } }\\ \\ \sf{\pink{squaring \: on \: both \: sides}} \\ \\ \implies \sf{ 1 = \red{85 + {c}^{2} } }\\ \\ \implies \sf{ {c}^{2} = 1 - 84} \\ \\ \implies \boxed{\sf{ c \: = \green{ \sqrt{ - 84} }}}$

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