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Question Number 5620 by sanusihammed last updated on 22/May/16

Find the resolved part of the vector a = 6i − 3j + 9k in the diection of b = 2i + 2j − k please help. i got the answer to be (−1)

$${Find}\:{the}\:{resolved}\:{part}\:{of}\:{the}\:{vector}\:{a}\:=\:\mathrm{6}{i}\:−\:\mathrm{3}{j}\:+\:\mathrm{9}{k}\: \\ $$$${in}\:{the}\:{diection}\:{of}\:{b}\:=\:\mathrm{2}{i}\:+\:\mathrm{2}{j}\:−\:{k} \\ $$$$ \\ $$$${please}\:{help}. \\ $$$$ \\ $$$${i}\:{got}\:{the}\:{answer}\:{to}\:{be}\:\left(−\mathrm{1}\right) \\ $$

Commented by prakash jain last updated on 22/May/16

1. Find angle between two vectors using the relation a∙b=∣a∣∣b∣ cos θ⇒cos θ=((a∙b)/(∣a∣∣b∣)) 2. Magnitude of resolution of a in direction of b=∣a∣cos θ 3. Direction of resolution is same as b so find unit vector in direction of b=(b/(∣b∣)) 4. Resolution of a in the direction of b =(magnitude of resolution from 3)× (unit vector in the direction of b from 4)

$$\mathrm{1}.\:\mathrm{Find}\:\mathrm{angle}\:\mathrm{between}\:\mathrm{two}\:\mathrm{vectors}\:\mathrm{using} \\ $$$$\:\:\:\:\:\mathrm{the}\:\mathrm{relation} \\ $$$$\:\:\:\:\:\boldsymbol{\mathrm{a}}\centerdot\boldsymbol{\mathrm{b}}=\mid\boldsymbol{\mathrm{a}}\mid\mid\boldsymbol{\mathrm{b}}\mid\:\mathrm{cos}\:\theta\Rightarrow\mathrm{cos}\:\theta=\frac{\boldsymbol{\mathrm{a}}\centerdot\boldsymbol{\mathrm{b}}}{\mid\boldsymbol{\mathrm{a}}\mid\mid\boldsymbol{\mathrm{b}}\mid} \\ $$$$\mathrm{2}.\:\mathrm{Magnitude}\:\mathrm{of}\:\mathrm{resolution}\:\mathrm{of}\:\boldsymbol{\mathrm{a}}\:\mathrm{in}\:\mathrm{direction} \\ $$$$\:\:\:\:\:\mathrm{of}\:\boldsymbol{\mathrm{b}}=\mid\boldsymbol{\mathrm{a}}\mid\mathrm{cos}\:\theta \\ $$$$\mathrm{3}.\:\mathrm{Direction}\:\mathrm{of}\:\mathrm{resolution}\:\mathrm{is}\:\mathrm{same}\:\mathrm{as}\:\boldsymbol{\mathrm{b}} \\ $$$$\:\:\:\:\:\mathrm{so}\:\mathrm{find}\:\mathrm{unit}\:\mathrm{vector}\:\mathrm{in}\:\mathrm{direction}\:\mathrm{of}\:\boldsymbol{\mathrm{b}}=\frac{\boldsymbol{\mathrm{b}}}{\mid\boldsymbol{\mathrm{b}}\mid} \\ $$$$\mathrm{4}.\:\mathrm{Resolution}\:\mathrm{of}\:\boldsymbol{\mathrm{a}}\:\mathrm{in}\:\mathrm{the}\:\mathrm{direction}\:\mathrm{of}\:\boldsymbol{\mathrm{b}} \\ $$$$\:\:\:\:\:=\left(\mathrm{magnitude}\:\mathrm{of}\:\mathrm{resolution}\:\mathrm{from}\:\mathrm{3}\right)× \\ $$$$\:\:\:\:\:\:\:\:\:\left(\mathrm{unit}\:\mathrm{vector}\:\mathrm{in}\:\mathrm{the}\:\mathrm{direction}\:\mathrm{of}\:\boldsymbol{\mathrm{b}}\:\mathrm{from}\:\mathrm{4}\right) \\ $$

Commented by prakash jain last updated on 22/May/16

Your answer is a scalar while you will need to get a vector.

$$\mathrm{Your}\:\mathrm{answer}\:\mathrm{is}\:\mathrm{a}\:\mathrm{scalar}\:\mathrm{while}\:\mathrm{you}\:\mathrm{will}\:\mathrm{need} \\ $$$$\mathrm{to}\:\mathrm{get}\:\mathrm{a}\:\mathrm{vector}. \\ $$

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