Game:

Vector (2012)

Duration: 8:25

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Two vectors \( \vec{a} \) and \( \vec{b} \), add up to a vector \( \vec{c} \). When vector \( \vec{a} \) is made 3 times as long and vector \( \vec{b} \) is doubled in length, without changing their directions, then it is found that vector \( \vec{c} \) is also doubled in length, without change in direction. Then which of the following is true
[J \& K CET 2012]
(a) All three vectors must be parallel
(b) \( \vec{b} \) and \( \vec{c} \) must be parallel to each other, but \( \vec{a} \) need not be parallel to \( \vec{b} \) and \( \vec{c} \)
(c) \( \vec{a} \) and \( \vec{b} \) must be perpendicular to each other
(d) It is impossible for three non-zero vectors \( \vec{a}, \vec{b} \) and \( \vec{c} \) to have the property stated above
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