With respect to a rectangular Cartesian co-ordinate system three vectors are expressed as a - 4- - - b - -3 - - 2 - and c - -k- where - - and k- are unit vectors along the x- y and z axes respectively- The unit vector along the direction of sum of these vectors is

Given a = 4 î ĵ, b= 3 î + 2 ĵ, c = k̂ Sum of these vectors, r = a + b + c =4 î ĵ 3 î + 2ĵ k̂ = î + ĵ k̂ r̂ = r⃗|r⃗|= î + ĵ k̂√(1^2 + 1^2 +( 1)^2) r̂ = ...

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Byju's Answer

Standard XI

Physics

Addition and Subtraction in Unit Vector Notation

With respect ...

Question

With respect to a rectangular Cartesian co-ordinate system three vectors are expressed as $\to a = 4^i -^j, \to b = - 3^i + 2^j$ and $\to c = -^k$ where $^i,^j$ and $^k$ are unit vectors along the x, y and z axes respectively. The unit vector along the direction of sum of these vectors is

^r = \frac{1}{\sqrt{3}} (^i +^j -^k)

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^r = \frac{1}{\sqrt{2}} (^i +^j -^k)

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^r = \frac{1}{3} (^i +^j -^k)

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^r = \frac{1}{\sqrt{3}} (^i +^j +^k)

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Solution

The correct option is A $^r = \frac{1}{\sqrt{3}} (^i +^j -^k)$
Given $\to a = 4^i -^j, \to b = - 3^i + 2^j, \to c = -^k$
Sum of these vectors,
$\to r = \to a + \to b + \to c = 4^i -^j - 3^i + 2^j -^k =^i +^j -^k$
$^r = \frac{\to r}{| \to r |} = \frac{^i +^j -^k}{\sqrt{1^{2} + 1^{2} + (- 1)^{2}}}$
$^r = \frac{^i +^j -^k}{\sqrt{3}}$

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With respect to a rectangular Cartesian co-ordinate system three vectors are expressed as →a=4^i−^j,→b=−3^i+2^j and →c=−^k where ^i,^j and ^k are unit vectors along the x, y and z axes respectively. The unit vector along the direction of sum of these vectors is

The correct option is A ^r=1√3(^i+^j−^k)Given →a=4^i−^j, →b=−3^i+2^j, →c=−^k Sum of these vectors, →r=→a+→b+→c=4^i−^j−3^i+2^j−^k=^i+^j−^k ^r=→r|→r|=^i+^j−^k√12+12+(−1)2 ^r=^i+^j−^k√3

With respect to a rectangular Cartesian co-ordinate system three vectors are expressed as $\to a = 4^i -^j, \to b = - 3^i + 2^j$ and $\to c = -^k$ where $^i,^j$ and $^k$ are unit vectors along the x, y and z axes respectively. The unit vector along the direction of sum of these vectors is