16. Prove that the rectangular components of two equal vectors must be equal to each other.
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Answered by
9
When a vector is splitted into three component vectors at right angle to each other, the component vectors are called rectangular components of a vector.
Consider two vectors
A
⃗
and
B
⃗
in x,y and z plane, so their component vectors will be,
A
⃗
=Ax
i
ˆ
+Ay
j
ˆ
+Az
k
ˆ
and
B
⃗
=Bx
i
ˆ
+By
j
ˆ
+Bz
k
ˆ
We know that two vectors are said to be equal if they have equal magnitude and same direction. If the two vectors
A
⃗
and
B
⃗
are represented by two equal parallel lines drawn with same scale, having arrow heads in the same direction, then
A
⃗
and
B
⃗
are equal vectors i.e.,
A
⃗
=
B
⃗
or,
Ax
i
ˆ
+Ay
j
ˆ
+Az
k
ˆ
=Bx
i
ˆ
+By
j
ˆ
+Bz
k
ˆ
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Answered by
14
When a vector is splitted into three component vectors at right angle to each other, the component vectors are called rectangular components of a vector. Consider two vectors A ⃗ and B ⃗ in x,y and z plane, so their component vectors will be, A ⃗ =Ax i ˆ +Ay j ˆ +Az k ˆ and B ⃗ =Bx i ˆ +By j ˆ +Bz k ˆ We know that two vectors are said to be equal if they have equal magnitude and same direction. If the two vectors A ⃗ and B ⃗ are represented by two equal parallel lines drawn with same scale, having arrow heads in the same direction, then A ⃗ and B ⃗ are equal vectors i.e., A ⃗ = B ⃗ or, Ax i ˆ +Ay j ˆ +Az k ˆ =Bx i ˆ +By j ˆ +Bz k ˆ
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