show that area of triangle made by vector A and B is half of magnitude of their vector product
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Consider two vectors OK = vector ∣a∣and OM = vector∣b∣, inclined at an angle θ as shown in the following figure.
In △OMN, we can write the relation:
sinθ=
OM
MN
=
∣
∣
∣
∣
b
∣
∣
∣
∣
MN
⟹MN=
∣
∣
∣
∣
b
∣
∣
∣
∣
sinθ
∣
∣
∣
∣
a
×
b
∣
∣
∣
∣
=∣
a
∣
∣
∣
∣
∣
b
∣
∣
∣
∣
sinθ
=OK×MN
=2×
2
1
×OK×MN
=2× Area of △OMK
⟹ Area of △ OMK=
2
1
×
∣
∣
∣
∣
a
×
b
∣
∣
∣
HOPE IT HELPS U FRND.....
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