Question

a= i-2j+k and b=2i+2j+k .the component of b in the direction of a

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Answer 1

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Answer 2

Given:

In the question given vectors are

a =  i-2j+k

b = b=2i+2j+k

To Find:

The b in the direction of a

Solution:

To find the component of b in the direction of a we have to find the dot product of unit vector of a with vector b.

Unit vector of any vector can be calculate by dividing the vector by the magnitude of the vector. Mathematically, for vector a,

                                                $\bold {\hat a} = \frac{\bold{a}}{|\bold{a}|}$

∴ Unit vector of a ($\bold {\hat a}$) = $\frac{\hat i - 2 \hat j +\hat k}{\sqrt{1^{2} +(-2)^{2} +1^{2} } }$ = $\frac{\hat i - 2 \hat j +\hat k}{\sqrt{6 } }$

∴ The component of b in the direction of a = $\bold{b} \bold{\hat a}$ = $(2 \hat i +2\hat j +\hat k) . (\frac{\hat i - 2 \hat j +\hat k}{\sqrt{6 } })$ = $\frac{-1}{\sqrt{6} }$

Hence the final answer is $\frac{-1}{\sqrt{6} }$