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In trapezoid ABCD, the base ratios BC/AD=8. Taking the vectors AC, BD as the basis, find the coordinates of the vectors AB,BC,CD,DA.
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Class 12
>>Maths
>>Vector Algebra
>>Vector or Cross Product
>>In a trapezium, the vector BC = lambda
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In a trapezium, the vector
BC
=λ
AD
and
P
=
AC
+
BD
=μ
AD
, then
Medium
Solution
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Correct option is A)
AC
+
BD
=(
AD
+
DC
)+(
AD
−
AB
)
=2
AD
+
DC
−
AB
Now,
AB
=
DB
′
Hence, 2
AD
+
DC
−
AB
=2
AD
+
DC
−
DB
′
Consider triangle DCB'
=2
AD
+
DC
−(
DC
+
CB
′
)
=2
AD
−
CB
′
=2
AD
−(
BB
′
−
BC
)
=2
AD
−(
AD
−
BC
)
=
AD
+
BC
=
AD
+λ
AD
=(1+λ)
AD
Hence,
μ
AD
=(1+λ)
AD
μ=1+λ
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