de. Refine Diagonalizable materise.
5. Evaluate sloga
dx
6. Evaluate lazent de
xeduction formula for
7. write
I sinn de
8. Evluate if he sint x cosPx de
o
9. find the equation of the plane
thorough (3,4,5) parallel to the
plane 24 - 3 4 -z=0
Answers
Answered by
1
Answer:
Vector equation of a plane passing through three points with position vectors
a
,
b
,
c
is
(
r
−
a
).[(
b
−
a
)×(
c
−
a
)]=0
Now, the plane passes through the points
A(2,3,4),B(−3,5,1) and C(4,−1,2)
b
−
a
=−3
i
^
+5
j
^
+
k
^
−2
i
^
−3
j
^
−4
k
^
=−5
i
^
+2
j
^
−3
k
^
c
−
a
=4
i
^
−
j
^
+2
k
^
−2
i
^
−3
j
^
−4
k
^
=2
i
^
−4
j
^
−2
k
^
(
b
−
a
)×(
c
−
a
)=
∣
∣
∣
∣
∣
∣
∣
∣
i
^
−5
2
j
^
2
−4
k
^
−3
−2
∣
∣
∣
∣
∣
∣
∣
∣
=(−4−12)
i
^
−(10+6)
j
^
+(20−4)
k
^
=−16
i
^
−16
j
^
+16
k
^
∴vector equation of plane is (x
i
^
+y
j
^
+z
k
^
−2
i
^
−3
j
^
−4
k
^
)(8
i
^
−16
j
^
−16
k
^
)=0
⇒[(x−2)
i
^
+(y−3)
j
^
+(z−4)
k
^
](8
i
^
−16
j
^
−16
k
^
)=0
⇒8x−16−16y+48−16z+64=0
⇒8x−16y−16z+96=0
or
x−2y−2z+12=0 is the required equation of the plane
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