
The area of triangle whose vertices are (1, 2, 3), (2, 5, −1) and (−1, 1, 2) is
150 sq. units
145 sq. units
sq. units
sq. units
Answer
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Hint: All three vertices of the triangle are given. We have to find the vector AB and AC which represents the side vectors. Using the concept of cross product, we have to find cross product of the vector AB and AC. By using the formula of area of triangle, we can simply find the area of triangle ABC. The formula of area of triangle is given below:
Area of triangle
Complete step-by-step solution -
Given: The vertices of the triangle are:
A (1, 2, 3), B (2, 5, -1) and C (-1, 1, 2)
Consider the origin to be at (0, 0). Now, is the difference of from .
Similarly, the is the difference of from
Then, the cross product of and is:
The magnitude of a resultant vector , can be expanded as:
Now, by using the above-mentioned expression, the magnitude of both the vectors,
Now, area of the triangle ABC
Area of the triangle ABC sq. units.
Hence, the area of the triangle ABC is sq. units.
Therefore, option (c) is correct.
Note: The key concept involved in solving this problem is the expression of sides in the form of vectors. Students must be careful while calculating the cross product and must be aware of the intricacies of signs involved in cross product. General mistake is done in the calculation of cross product.
Area of triangle
Complete step-by-step solution -

Given: The vertices of the triangle are:
A (1, 2, 3), B (2, 5, -1) and C (-1, 1, 2)
Consider the origin to be at (0, 0). Now,
Similarly, the
Then, the cross product of
The magnitude of a resultant vector
Now, by using the above-mentioned expression, the magnitude of both the vectors,
Now, area of the triangle ABC
Area of the triangle ABC
Hence, the area of the triangle ABC is
Therefore, option (c) is correct.
Note: The key concept involved in solving this problem is the expression of sides in the form of vectors. Students must be careful while calculating the cross product and must be aware of the intricacies of signs involved in cross product. General mistake is done in the calculation of cross product.
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