With respect to a rectangular cartesian coordinate system- three vectors are expressed as a-4-b-3-2- andc-k- where - k- are unit vectors- along the X- Y and Z-axis respectively- The unit vectors r-along the direction of sum of these vector is

R⃗=a⃗+b⃗+c⃗=4î ĵ 3î+2ĵ k̂=î+ĵ k̂ r̂=r⃗/|r|=î+ĵ k̂/√(1^2+1^2+( 1)^2)=î+ĵ k̂/√(3). ...

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Byju's Answer

Standard XII

Physics

Addition and Subtraction in Unit Vector Notation

With respect ...

Question

With respect to a rectangular cartesian coordinate system, three vectors are expressed as $\to a = 4^i -^j, \to b = - 3^i + 2^j$ and
$\to c = -^k$ where $^i,^j,^k$ are unit vectors, along the X, Y and Z-axis respectively. The unit vectors $^r$ along the direction of sum of these vector 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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$^r = \frac{1}{\sqrt{3}} (^i -^j +^k)$

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

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Solution

The correct option is A
$^r = \frac{1}{\sqrt{3}} (^i +^j -^k)$

$\to r = \to a + \to b + \to c = 4^i -^j - 3^i + 2^j -^k =^i +^j -^k$
$^r = \frac{\to r}{| r |} = \frac{^i +^j -^k}{\sqrt{1^{2} + 1^{2} + (- 1)^{2}}} = \frac{^i +^j -^k}{\sqrt{3}}$ .

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With respect to a rectangular cartesian coordinate system, three vectors are expressed as →a=4^i−^j,→b=−3^i+2^j and →c=−^k where ^i,^j,^k are unit vectors, along the X, Y and Z-axis respectively. The unit vectors ^ralong the direction of sum of these vector is

The correct option is A ^r=1√3(^i+^j−^k) →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=^i+^j−^k√3.

With respect to a rectangular cartesian coordinate system, three vectors are expressed as $\to a = 4^i -^j, \to b = - 3^i + 2^j$ and
$\to c = -^k$ where $^i,^j,^k$ are unit vectors, along the X, Y and Z-axis respectively. The unit vectors $^r$ along the direction of sum of these vector is

The correct option is A
$^r = \frac{1}{\sqrt{3}} (^i +^j -^k)$

$\to r = \to a + \to b + \to c = 4^i -^j - 3^i + 2^j -^k =^i +^j -^k$
$^r = \frac{\to r}{| r |} = \frac{^i +^j -^k}{\sqrt{1^{2} + 1^{2} + (- 1)^{2}}} = \frac{^i +^j -^k}{\sqrt{3}}$ .