find vector equation of plane passing through A(-2,7,5)and parallel to the vector 4i+-j+3k and i+j+k and also find the Cartesian equation
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The line passes through the point,
a
=2
i
^
+3
j
^
+
k
^
And parallel to the line,
b
=4
i
^
−2
j
^
+3
k
^
The vector equation of the line passing through a point and parallel to the given line is,
r
=
a
+λ
b
Substituting the values, we get,
r
=(2
i
^
+3
j
^
+
k
^
)+λ(4
i
^
−2
j
^
+3
k
^
)
r
=(2+4λ)
i
^
+(3−2λ)
j
^
+(1+3λ)
k
^
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