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Question
AB
=
3
i
^
+
2
j
^
-
k
^
and AC
=
5
i
^
-
j
^
+
2
k
^
are the two side of a parallelogram. Find the area of the parallelogram.
17
.
748
sq. units
13
.
379
sq. units
17
.
2916
sq. units
None of the above
ANSWER : 3
Descrption
<p style="margin-left:0px;"><br>The area of a parallelogram can be calculated using the cross product of its adjacent sides. Given the vectors representing the sides AB and AC:</p><ul><li>AB = 3i + 2j - k</li><li>AC = 5i - j + 2k</li></ul><p style="margin-left:0px;">The area of the parallelogram is the magnitude of the cross product of these vectors:</p><p>Area = ||AB x AC|| Area = ||(3i + 2j - k) x (5i - j + 2k)|| Area = ||(6i + 7j - 11k)|| Area = sqrt(6^2 + 7^2 + (-11)^2) Area = sqrt(214) ≈ 17.2916 sq. units </p><p style="margin-left:0px;">Therefore, the area of the parallelogram is approximately <strong>17.2916 square units</strong>.</p>
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