If the points A(1,2, 3) B(-1, 1,2) C(2,3, 4) and D(-1, x, 0) are co planer find the value of x
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studying in class VI of MODEL PUBLIC SCHOOL. You have lost your English Text in school. Draft a notice to be put up on the school notice board giving details of the book and offering a suitable reward. Use not more than 50 words.You are Ankit / Ankita studying in class VI of MODEL
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Let
OA
=3
i
^
+2
j
^
+
k
^
;
OB
=4
i
^
+x
j
^
+5
k
^
OC
=4
i
^
+2
j
^
−2
k
^
;
OD
=6
i
^
+5
j
^
−
k
^
∴
AB
=
OB
−
OA
=
i
^
+(x−2)
j
^
+4
k
^
AC
=
OC
−
OA
=
i
^
+0
j
^
−3
k
^
AD
=
OD
−
OA
=3
i
^
+3
j
^
−2
k
^
To find x, given vectors are coplanar
=[
AB
AC
AD
]=0
∣
∣
∣
∣
∣
∣
∣
∣
1
1
3
x−2
0
3
4
−3
−2
∣
∣
∣
∣
∣
∣
∣
∣
=0
Expanding the determinant
⇒1(0+9)−(x−2)(−2+9)+4(3−0)=0
⇒9−(x−2)(7)+12=0
or −7x+14+21=0
⇒−7x=−35
or x=5.
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