If |ā| = 2, |b| = 5, and ā. b = 8 then |a-b| =
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Class 12
>>Maths
>>Vector Algebra
>>Scalar or Dot Product
>>If | a | = 2, | b | = 5 and | a × b |
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If ∣
a
∣=2,
∣
∣
∣
b
∣
∣
∣
=5 and
∣
∣
∣
a
×
b
∣
∣
∣
=8, find
a
.b =5
∣
a
ˉ
∣=2,∣
b
ˉ
∣=5
∣
a
ˉ
×
b
ˉ
∣=8
Consider ∣
a
ˉ
×
b
ˉ
∣=∣
a
ˉ
∣⋅∣
b
ˉ
∣⋅sinθ
⇒8=2⋅5sinθ
⇒
10
8
=sinθ
sinθ=
5
4
θ=sin
−1
(
5
4
)
a
ˉ
⋅
b
ˉ
=∣
a
ˉ
∣⋅∣
b
ˉ
∣cosθ
=2⋅5cos[sin
−1
(
5
4
)]
=10cos[cos
−1
(
5
3
)]
=10×
5
3
=6
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