The two adjacent sides of a parallelogram are 2i-4j+5k and i-2j-3k. find the unit vector parallel to its diagonal.also find its area
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The unit vector to the diagonal is (3i - 6j + 2k) / 7 and the area of the parallelogram is 11 (5)^0.5
The diagonal of a parallelogram whose adjacent sides a and b are given, is calculated using the formula:
a + b (where both a and b should be in vector notation)
a + b = (i-2j-3k) + (2i-4j+5k)
a + b = 3i - 6j + 2k
Magnitude of a + b is 7
Hence unit vector to the diagonal is (3i - 6j + 2k) / 7
Area of parallelogram is given by formula:
A = 0.5 [a x b]
A = 0.5 [22i + 11j]
A = 11 (5)^0.5
The diagonal of a parallelogram whose adjacent sides a and b are given, is calculated using the formula:
a + b (where both a and b should be in vector notation)
a + b = (i-2j-3k) + (2i-4j+5k)
a + b = 3i - 6j + 2k
Magnitude of a + b is 7
Hence unit vector to the diagonal is (3i - 6j + 2k) / 7
Area of parallelogram is given by formula:
A = 0.5 [a x b]
A = 0.5 [22i + 11j]
A = 11 (5)^0.5
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