Given a vector field F-y2x-x-yz-y-x2-z-the line integral -F-d-l- evaluated along a segment on the x-axis from x- 1 to x- 2 is

F⃗=y^2xâ_x yz â_̂ŷ x^2â_̂ẑ and nbsp; nbsp;dl⃗ = dxâ_̂x̂+dyâ_̂ŷ+dzâ_̂ẑ F⃗.dl⃗ = y^2xdx yz dy x^2dz on x axis, y = 0, z = 0 ⇒ nbsp;F⃗.dl⃗ = 0 ∫_x=1^x=2F⃗. ...

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Engineering Mathematics

Line Integrals I

Given a vecto...

Question

Given a vector field $\to F = y^{2} x {^a}_{x} - y z {^a}_{y} - x^{2} {^a}_{z}$ ,the line integral $\int \to F . \to d l$ evaluated along a segment on the x-axis from x= 1 to x= 2 is

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Solution

The correct option is B 0
$\to F = y^{2} x {^a}_{x} - y z_{y} - x^{2}_{z}$
and $d \to l = d x_{x} + d y_{y} + d z_{z}$
$\to F . d \to l = y^{2} x d x - y z d y - x^{2} d z$
on x-axis, y = 0, z = 0
$\Rightarrow$ $\to F . d \to l$ = 0
$\int_{x = 1}^{x = 2} \to F . d \to l = 0$

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Given a vector field →F=y2x^ax−yz^ay−x2^az,the line integral ∫→F.→dl evaluated along a segment on the x-axis from x= 1 to x= 2 is

The correct option is B 0→F=y2x^ax−yz^ay−x2^az and d→l=dx^ax+dy^ay+dz^az →F.d→l=y2xdx−yz dy−x2dz on x-axis, y = 0, z = 0 ⇒ →F.d→l = 0 ∫x=2x=1→F.d→l=0

Given a vector field $\to F = y^{2} x {^a}_{x} - y z {^a}_{y} - x^{2} {^a}_{z}$ ,the line integral $\int \to F . \to d l$ evaluated along a segment on the x-axis from x= 1 to x= 2 is

The correct option is B 0
$\to F = y^{2} x {^a}_{x} - y z_{y} - x^{2}_{z}$
and $d \to l = d x_{x} + d y_{y} + d z_{z}$
$\to F . d \to l = y^{2} x d x - y z d y - x^{2} d z$
on x-axis, y = 0, z = 0
$\Rightarrow$ $\to F . d \to l$ = 0
$\int_{x = 1}^{x = 2} \to F . d \to l = 0$