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Vector Algebra ...

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  • Question 1
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    If a and b are two non-zero and non-collinear vectors, then a + b and a - b are

  • Question 2
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    Let P, Q, R and S be the points on the plane with position vectors (-2i - j), 4i, (3i + 3j) and (-3i + 2j) respectively. The quadilateral PQRS must be a

  • Question 3
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    In triangle ABCABC, which of the following is not true?

  • Question 4
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    a  0ˉ,b0ˉ,c0,a×b=0, bˉ×c=0a×c=\vec{a}\, \neq\, \bar{0},\,\vec{b}\,\neq\,\bar{0},\,\vec{c}\,\neq\,0,\,\vec{a}\,\times\,\vec{b}\,=\,\vec{0},\, \bar{b}\,\times\,\vec{c}\,=\,0\,\Rightarrow\,\vec{a}\,\times\,\vec{c}\,=

  • Question 5
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    The position vectors of PP and QQ are respectively aa and bb. If RR is a point on PQPQ, PQPQ such that PR=5PQPR=5PQ, then the position vector of RR is

  • Question 6
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    If a=b=1|\vec {a}| = |\vec {b}| = 1 and a+ b=3|\vec {a} + \vec {b}| = \sqrt {3}, then the value of (3a4b)(2a+5b)(3\vec {a} - 4\vec {b}) \cdot (2\vec {a} + 5\vec {b}) is

  • Question 7
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    Let a= i+2j+ k, b= i j+ k\vec {a} = \vec {i} + 2\vec {j} + \vec {k}, \vec {b} = \vec {i} - \vec {j} + \vec {k} and c= i+ j k\vec {c} = \vec {i} + \vec {j} - \vec {k}. A vector in the plane of a\vec {a} and b\vec {b} has projection $$\dfrac {1}{\sqrt {3}}  \ on\  \vec {c}$$. Then, one such vector is

  • Question 8
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    Let a, b\overrightarrow {a} , \overrightarrow {b} and c\overrightarrow {c} be vectors with magnitudes 3, 4 and 5 respectively and a+ b+c=0\overrightarrow{a} + \overrightarrow {b}+\overrightarrow {c}=\overrightarrow {0}, then the value of a. b+b. c+ c. a\overrightarrow{a}. \overrightarrow{b}+\overrightarrow{b}. \overrightarrow{c} + \overrightarrow{c}. \overrightarrow{a} is

  • Question 9
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    Find the correct vectorial relationship with the help of the figure above.

  • Question 10
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    How much does a watch lose per day, if its hands coincide every 6464 minutes?

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