show that vector product of two vector in terms of their rectangular component can be written in the form of determinant
Answers
Answered by
0
Explanation:
Let there be two vector
a
and
b
subtending an angle θ, and θ
2
with horizontal respectively.
Thus by scalar product formula,
a
.
b
=abcos(θ
2
−θ
1
) ...(1)
Now by protection their rectangular components
a
=∣
a
∣cosθ
1
+∣
a
∣sinθ
1
b
=∣
b
∣cosθ
1
+∣
b
∣sinθ
2
Now,
a
.
b
=(acosθ
1
+asinθ
1
)(bcosθ
2
+bsinθ
2
)
a
.
b
=abcosθ
1
.cosθ
2
+absinθ
1
.sinθ
2
a
.
b
=ab(cosθ
1
.cosθ
2
+sinθ
1
.sinθ
2
)
a
.
b
=abcos(θ
2
−θ
1
) proved
solution
expand
Similar questions