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Question
Consider points A, B, C and D with position vectors<6,−4,7>,<1,−6,10>,<−1,−3,4> and <5,−1,5> respectively. Then ABCD is a
Consider points A, B, C and D with position vectors<6,−4,7>,<1,−6,10>,<−1,−3,4> and <5,−1,5> respectively. Then ABCD is a
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Solution
The correct option is D none of these
We are given four points. The position vectors of four vectors in fact. Now looking at the options I can conclude that it can be solved by finding the sides of the quadrilateral. If we can’t conclude anything from the side lengths, we then would need to see what the angles formed by the sides are. Since the position vectors of the vertices are given let’s write the coordinates of these points.
A (6,-4,7) B(1,-6,10) C (-1, -3, 4) and D (5, -1, 5)
Now finding the sides,
AB=7; CD=√47; BC=7; DA=√17
Since all these sides are dissimilar we can instantly eliminate the options (a), (b) and (c). So the correct answer would be (d) or none of these.
We are given four points. The position vectors of four vectors in fact. Now looking at the options I can conclude that it can be solved by finding the sides of the quadrilateral. If we can’t conclude anything from the side lengths, we then would need to see what the angles formed by the sides are. Since the position vectors of the vertices are given let’s write the coordinates of these points.
A (6,-4,7) B(1,-6,10) C (-1, -3, 4) and D (5, -1, 5)Now finding the sides,
AB=7; CD=√47; BC=7; DA=√17
Since all these sides are dissimilar we can instantly eliminate the options (a), (b) and (c). So the correct answer would be (d) or none of these.
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