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Mathematics
Problem
For two vectors
A
=
A
x
i
^
+
A
y
j
^
\mathbf{A}=A_x\hat{i}+A_y\hat{j}
A
=
A
x
i
^
+
A
y
j
^
and
B
=
B
x
i
^
+
B
y
j
^
\mathbf{B}=B_x\hat{i}+B_y\hat{j}
B
=
B
x
i
^
+
B
y
j
^
, which of the following gives the vector sum
A
+
B
\mathbf{A}+\mathbf{B}
A
+
B
? a)
(
A
x
−
B
x
)
i
^
+
(
A
y
−
B
y
)
j
^
(A_x-B_x)\hat{i}+(A_y-B_y)\hat{j}
(
A
x
−
B
x
)
i
^
+
(
A
y
−
B
y
)
j
^
b)
(
A
x
+
B
x
)
i
^
+
(
A
y
+
B
y
)
j
^
(A_x+B_x)\hat{i}+(A_y+B_y)\hat{j}
(
A
x
+
B
x
)
i
^
+
(
A
y
+
B
y
)
j
^
c)
(
A
x
+
B
y
)
i
^
+
(
A
y
+
B
x
)
j
^
(A_x+B_y)\hat{i}+(A_y+B_x)\hat{j}
(
A
x
+
B
y
)
i
^
+
(
A
y
+
B
x
)
j
^
d)
(
A
x
B
x
)
i
^
+
(
A
y
B
y
)
j
^
(A_xB_x)\hat{i}+(A_yB_y)\hat{j}
(
A
x
B
x
)
i
^
+
(
A
y
B
y
)
j
^
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