Find the Cartesian equation of the following plane:
$r . (2^i + 3^j - 4^k) = 1$

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Solution

Given vector equation is $r . (2^i + 3^j - 4^k) = 1$ ...(ii)

for any arbitrary point P(x,y,z) on the plane , position vector r is given by $x^i + y^j + z^k$

Substituting the value of r in Eq. (ii), we obtain

$(x^i + y^j + z^k) . (2^i + 3^j - 4^k) = 1 \Rightarrow 2 x + 3 y - 4 z = 1$

which is the required Cartesian form.

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\to r \cdot (2^i + 3^j - 4^k) = 1

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