With respect to a rectangular cartesian coordinates system- three vectors are expressed as a- - 4 - - - - b- - - 3 i - 2 - and c- and -k- where - - - - k- are unit vectors- along the direction of sum of these vector is -

The vector sum is given as, #10; #10; r⃗ = a⃗ + #10;b⃗ + c⃗ #10; #10; r⃗ = 4î #10;ĵ 3î + 2ĵ k̂ #10; #10; r⃗ = î + #10;ĵ ...

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Byju's Answer

Standard XII

Physics

Vector Addition

With respect ...

Question

With respect to a rectangular cartesian coordinates system, three vectors are expressed as $\to a = 4^i -^j, \to b + - 3 i + 2^j$ and $\to c$ and $^- k$ where $^i,^j,^k$ are unit vectors, along the direction of sum of these vector is :

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Solution

The vector sum is given as,

$\to r = \to a + \to b + \to c$

$\to r = 4^i -^j - 3^i + 2^j -^k$

$\to r =^i +^j -^k$

The unit vector is given as,

$\to R = \frac{\to r}{| \to r |}$

$\to R = \frac{^i +^j -^k}{\sqrt{1 + 1 + 1}}$

$\to R = \frac{^i +^j -^k}{\sqrt{3}}$

The unit vector is $\frac{^i +^j -^k}{\sqrt{3}}$ .

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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
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