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Vector Algebra

One Word Answers

11. Classify the following measures as scalars and vectors.
distance

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12. Classify the following measures as scalars and vectors.
force

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13. Classify the following measures as scalars and vectors.
velocity

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14. Classify the following measures as scalars and vectors.
work done

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Short Answer Type

15. In figure, (a square), identify the following vectors.

(i) Coinitial
(ii) Equal
(iii) Collinear but not equal

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16. In given figure which of the vectors are:

(i) Collinear (ii) Equal (iii) Coinitial

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True Or False

17. Answer the following as true or false.

straight a with rightwards arrow on top space space and space minus straight a with rightwards arrow on top

are collinear.

Two collinear vectors are always equal in magnitude.

Two vectors having same magnitude are collinear.

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Short Answer Type

18.

If $open vertical bar straight a with rightwards arrow on top close vertical bar space equals space 3 space and space space minus space 4 space less or equal than space straight k space less or equal than space 1 comma$ then what can you say about $open vertical bar straight k space straight a with rightwards arrow on top close vertical bar$ ?

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19. A, B and C are three collincar points such that

AB with rightwards arrow on top space equals space straight a with rightwards arrow on top space and space BC with rightwards arrow on top space equals straight b with rightwards arrow on top

. Find the vector

AC with rightwards arrow on top

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20. $straight a with rightwards arrow on top space and space straight b with rightwards arrow on top$ are two non-collinear vectors having the same initial point. What vectorn is represented by $straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top$ ?

Let $OA with rightwards arrow on top space equals space straight a with rightwards arrow on top comma space space space OB with rightwards arrow on top space equals space straight b with rightwards arrow on top$
$therefore space space space space space space AC with rightwards arrow on top space equals space OB with rightwards arrow on top space equals space straight b with rightwards arrow on top$
Now, $OC with rightwards arrow on top space equals space OA with rightwards arrow on top space plus space AC with rightwards arrow on top$
$therefore space space space space OC with rightwards arrow on top space equals space straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top$
$therefore space space space space straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top$ is the vector represented by the diagonal OC.