LCM of a=2×3×5, b=2^×3^×5, c=2×3×5^ is : a=900 b=30 , c=2
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Class 12
>>Maths
>>Vector Algebra
>>Vector or Cross Product
>>If A (3, 2, 1), B ( - 2, 2, - 3), C (3,
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If A (3, 2, 1), B (−2, 2, −3), C (3, 5, −2), D (−2, 5, −4)
then find its area.
Medium
Solution
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AB
=
b
ˉ
−
a
ˉ
=(−2
i
^
+2
j
^
−3
k
^
)−(3
i
^
+2
j
^
−
k
^
)
=−5
i
^
−2
k
^
AD
=
d
ˉ
−
a
ˉ
=(−2
i
^
+5
j
^
−4
k
^
)−(3
i
^
+2
j
^
−
k
^
)
=−5
i
^
+3
j
^
−3
k
^
AB
×
AD
=
∣
∣
∣
∣
∣
∣
∣
∣
i
^
−5
−5
j
^
0
3
k
^
−2
−3
∣
∣
∣
∣
∣
∣
∣
∣
=(0+6)
i
^
−(15−10)
j
^
+(−15+0)
k
^
=6
i
^
−5
j
^
−15
k
^
∴ area of parallelogram =
∣
∣
∣
AB
×
AD
∣
∣
∣
=
6
2
+(−5)
2
+(−15)
2
36+25+255
=
286
sq units.
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