Question

calculate the value of k cap .I cap
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Answer 1

$\underline{\textsf{Given:}}$

$\mathsf{\hat{i}\;}\textsf{and}\;\mathsf{\hat{k}\;}$

$\underline{\textsf{To find:}}$

$\mathsf{\hat{k}.\hat{i}}$

$\underline{\textsf{Solution:}}$

$\textsf{Concept:}$

$\textsf{The scalar product of two vectors is}$

$\boxed{\mathsf{\vec{a}.\vec{b}=|\vec{a}|\;|\vec{b}|\;cos\theta}}$

$\textsf{We know that,}$

$\mathsf{\hat{i}}\;\textsf{and}\;\mathsf{\hat{k}}\;\textsf{are unit vectors along x and z axis}$

$\textsf{Now,}$

$\mathsf{\hat{k}.\hat{i}}$

$\mathsf{=|\hat{k}|\;|\hat{i}|\;cos90^{\circ}}$

$\mathsf{=(1)(1)(0)}$

$\mathsf{=0}$

$\underline{\textsf{Answer:}}$

$\mathsf{\hat{k}.\hat{i}=0}$

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Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

DOT PRODUCT

$\sf{Let \: \theta \: be \: the \: angle \: between \: two \: vectors \: \vec{a} \: and \: \vec{b}}$

Then the Dot product ( or scaler product) of the two is denoted by

$\sf{\vec{a} \: . \vec{b} \: \: and \: defined \: as \: }$

$\sf{\vec{a} \: . \vec{b} = | \: \vec{a} \: | | \: \vec{b} \: | \cos \theta \: }$

TO CALCULATE

$\sf{ \hat{k} \: . \: \hat{i} \: }$

CALCULATION

Here

$\sf{ \hat{k} \: and \: \hat{i} \: are \: unit \: vectors \: along \: oz \: and \: ox \: respectively\: }$

So they are perpendicular to each other

$\displaystyle \: \sf{ \: Therefore \: \: \: \theta \: = \frac{\pi}{2} \: }$

Hence

$\sf{ \hat{k} \: . \: \hat{i} \: }$

$\displaystyle \: = \sf{ |\hat{k} | \: |\hat{i}| \cos \frac{\pi}{2} \: }$

$= \sf{ \:1 \times 1 \times 0 \: }$

$= 0$

RESULT

$\boxed{ \sf{\: The \: required \: answer \: is \: \: \: 0 }\: }$

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