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Quiz 2
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Which one of the following can be written for (\(\vec{a}\) – \(\vec{b}\)) × (\(\vec{a}\) + \(\vec{b}\))
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\(\vec{a}\) × \(\vec{b}\)
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2\(\vec{a}\) × \(\vec{b}\)
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\(\vec{a}\)² – \(\vec{b}\)
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2\(\vec{b}\) × \(\vec{b}\)
Explanation
2\(\vec{a}\) × \(\vec{b}\)
The points with position vectors (6), (1, 2) and (a, 10) are collinear if the of a is
0%
-8
0%
4
0%
3
0%
12
Explanation
3
|\(\vec{a}\) + \(\vec{b}\)| = |\(\vec{a}\) – \(\vec{b}\)| then the angle between \(\vec{a}\) and \(\vec{b}\)
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\(\frac{π}{2}\)
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0
0%
\(\frac{π}{4}\)
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\(\frac{π}{6}\)
Explanation
\(\frac{π}{2}\)
|\(\vec{a}\) × \(\vec{b}\)| = |\(\vec{a}\).\(\vec{b}\)| then the angle between \(\vec{a}\) and \(\vec{b}\)
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0
0%
\(\frac{π}{2}\)
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\(\frac{π}{4}\)
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π
Explanation
0
If ABCDEF is a regular hexagon then \(\vec{AB}\) + \(\vec{EB}\) + \(\vec{FC}\) equals
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zero
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2\(\vec{AB}\)
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4\(\vec{AB}\)
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3\(\vec{AB}\)
Explanation
3\(\vec{AB}\)
Which one of the following is the modulus of x\(\hat{i}\) + y\(\hat{j}\) + z\(\hat{k}\)?
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\(\sqrt{x^2+y^2+z^2}\)
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\(\frac{1}{\sqrt{x^2+y^2+z^2}}\)
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x² + y² + z²
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none of these
Explanation
\(\sqrt{x^2+y^2+z^2}\)
If C is the mid point of AB and P is any point outside AB then,
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\(\vec{PA}\) + \(\vec{PB}\) = 2\(\vec{PC}\)
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\(\vec{PA}\) + \(\vec{PB}\) = \(\vec{PC}\)
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\(\vec{PA}\) + \(\vec{PB}\) = 2\(\vec{PC}\) = 0
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None of these
Explanation
\(\vec{PA}\) + \(\vec{PB}\) = 2\(\vec{PC}\)
If \(\vec{OA}\) = 2\(\vec{i}\) – \(\vec{j}\) + \(\vec{k}\), \(\vec{OB}\) = \(\vec{i}\) – 3\(\vec{j}\) – 5\(\vec{k}\) then |\(\vec{OA}\) × \(\vec{OB}\)| =
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8\(\vec{i}\) + 11\(\vec{j}\) – 5\(\vec{k}\)
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\(\sqrt{210}\)
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sin θ
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\(\sqrt{40}\)
Explanation
\(\sqrt{210}\)
If |a| = |b| = |\(\vec{a}\) + \(\vec{b}\)| = 1 then |\(\vec{a}\) – \(\vec{b}\)| is equal to
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1
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√3
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0
0%
None of these
Explanation
√3
If \(\vec{a}\) and \(\vec{b}\) are any two vector then (\(\vec{a}\) × \(\vec{b}\))² is equal to
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(\(\vec{a}\))²(\(\vec{b}\))² – (\(\vec{a}\).\(\vec{b}\))²
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(\(\vec{a}\))² (\(\vec{b}\))² + (\(\vec{a}\).\(\vec{b}\))²
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(\(\vec{a}\).\(\vec{b}\))²
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(\(\vec{a}\))²(\(\vec{b}\))²
Explanation
(\(\vec{a}\))²(\(\vec{b}\))² – (\(\vec{a}\).\(\vec{b}\))²
If \(\hat{a}\) and \(\hat{b}\) be two unit vectors and 0 is the angle between them, then |\(\hat{a}\) – \(\hat{b}\)| is equal to
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sin \(\frac{θ}{2}\)
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2 sin \(\frac{θ}{2}\)
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cos \(\frac{θ}{2}\)
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2 cos \(\frac{θ}{2}\)
Explanation
2 sin \(\frac{θ}{2}\)
The angle between the vector 2\(\hat{i}\) + 3\(\hat{j}\) + \(\hat{k}\) and 2\(\hat{i}\) – \(\hat{j}\) – \(\hat{k}\) is
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\(\frac{π}{2}\)
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\(\frac{π}{4}\)
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\(\frac{π}{3}\)
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0
Explanation
\(\frac{π}{2}\)
If \(\vec{a}\) = \(\hat{i}\) – \(\hat{j}\) + \(\hat{k}\), \(\vec{b}\) = \(\hat{i}\) + 2\(\hat{j}\) – \(\hat{k}\), \(\vec{c}\) = 3\(\hat{i}\) – p\(\hat{j}\) – 5\(\hat{k}\) are coplanar then P =
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6
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-6
0%
2
0%
-2
Explanation
6
The distance of the point (- 3, 4, 5) from the origin
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50
0%
5√2
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6
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None of these
Explanation
5√2
If \(\vec{AB}\) = 2\(\hat{i}\) + \(\hat{j}\) – 3\(\hat{k}\) and the co-ordinates of A are (1, 2, -1) then coordinate of B are
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(2, 2, -3)
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(3, 2, -4)
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(4, 2, -1)
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(3, 3, -4)
Explanation
(3, 3, -4)
If \(\vec{b}\) is a unit vector in xy-plane making an angle of \(\frac{π}{4}\) with x-axis. then \(\vec{b}\) is equal to
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\(\hat{i}\) + \(\hat{j}\)
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\(\vec{i}\) – \(\vec{j}\)
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\(\frac{\vec{i}+\vec{j}}{√2}\)
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\(\frac{\vec{i}-\vec{j}}{√2}\)
Explanation
\(\frac{\vec{i}+\vec{j}}{√2}\)
\(\vec{a}\) = 2\(\hat{i}\) + \(\hat{j}\) – 8\(\hat{k}\) and \(\vec{b}\) = \(\hat{i}\) + 3\(\hat{j}\) – 4\(\hat{k}\) then the magnitude of \(\vec{a}\) + \(\vec{b}\) is equal to
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13
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\(\frac{13}{4}\)
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\(\frac{3}{13}\)
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\(\frac{4}{13}\)
Explanation
13
The vector in the direction of the vector \(\hat{i}\) – 2\(\hat{j}\) + 2\(\hat{k}\) that has magnitude 9 is
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\(\hat{i}\) – 2\(\hat{j}\) + 2\(\hat{k}\)
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\(\frac{\hat{i}-2\hat{j}+2\hat{k}}{3}\)
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3(\(\hat{i}\) – 2\(\hat{j}\) + 2\(\hat{k}\))
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9(\(\hat{i}\) – 2\(\hat{j}\) + 2\(\hat{k}\))
Explanation
3(\(\hat{i}\) – 2\(\hat{j}\) + 2\(\hat{k}\))
The position vector of the point which divides the join of points 2\(\vec{a}\) – 3\(\vec{b}\) and \(\vec{a}\) + \(\vec{b}\) in the ratio 3 : 1 is
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\(\frac{3\vec{a}-2\vec{b}}{2}\)
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\(\frac{7\vec{a}-8\vec{b}}{2}\)
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\(\frac{3\vec{a}}{2}\)
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\(\frac{5\vec{a}}{4}\)
Explanation
\(\frac{5\vec{a}}{4}\)
The vector having, initial and terminal points as (2, 5, 0) and (- 3, 7, 4) respectively is
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–\(\hat{i}\) + 12\(\hat{j}\) + 4\(\hat{k}\)
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5\(\hat{i}\) + 2\(\hat{j}\) – 4\(\hat{k}\)
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-5\(\hat{i}\) + 2\(\hat{j}\) + 4\(\hat{k}\)
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\(\hat{i}\) + \(\hat{j}\) + \(\hat{k}\)
Explanation
-5\(\hat{i}\) + 2\(\hat{j}\) + 4\(\hat{k}\)
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