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Vector Algebra
Quiz 4
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The vectors \(\vec{a}\) = x\(\hat{i}\) – 2\(\hat{j}\) + 5\(\hat{k}\) and \(\vec{b}\) = \(\hat{i}\) + y\(\hat{j}\) – z\(\hat{k}\) are collinear, if
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x = 1, y = -2, z = -5
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x = \(\frac{3}{2}\), y = -4, z = -10
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x = \(\frac{3}{2}\), y = 4, z = 10
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All of these
Explanation
All of these
The vectors (x, x + 1, x + 2), (x + 3, x + 4, x + 5) and (x + 6, x + 7, x + 8) are coplanar for
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all values of x
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x < 0
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x ≤ 0
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None of these
Explanation
all values of x
The vectors \(\vec{AB}\) = 3\(\hat{i}\) +4\(\hat{k}\) and \(\vec{AC}\) = 5\(\hat{i}\) – 2\(\hat{j}\) + 4\(\hat{k}\) are the sides of ΔABC. The length of the median through A is
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\(\sqrt{18}\)
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\(\sqrt{72}\)
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\(\sqrt{33}\)
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\(\sqrt{288}\)
Explanation
\(\sqrt{33}\)
The summation of two unit vectors is a third unit vector, then the modulus of the difference of the unit vector is
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√3
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1 – √3
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1 + √3
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-√3
Explanation
√3
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