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The vector represents the required displacement.

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Vector Algebra

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

We have $AC with rightwards arrow on top space equals space AB with rightwards arrow on top space plus space BC with rightwards arrow on top$
$therefore$ $AC with rightwards arrow on top space equals space straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top$

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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 $open vertical bar straight k space straight a with rightwards arrow on top close vertical bar$ ?

Here,    $open vertical bar straight a with rightwards arrow on top close vertical bar space equals space 3 comma space space space space minus space 4 space less or equal than space straight k space less or equal than space 1$
When k = -4,    $open vertical bar straight k space straight a with rightwards arrow on top close vertical bar space equals space open vertical bar straight k space straight a with rightwards arrow on top close vertical bar space equals space open vertical bar straight k close vertical bar space open vertical bar straight a with rightwards arrow on top close vertical bar space equals negative open vertical bar negative 4 space left enclose left parenthesis 3 end enclose right parenthesis close vertical bar space equals space 4 space cross times space 3 space equals space 12$
When k = 1,    $open vertical bar straight k space straight a with rightwards arrow on top close vertical bar space equals space open vertical bar straight k close vertical bar space open vertical bar straight a with rightwards arrow on top close vertical bar space equals space left parenthesis 1 right parenthesis thin space left parenthesis 3 right parenthesis space equals space 3$
Also,
   $open vertical bar straight k space straight a with rightwards arrow on top close vertical bar space space greater or equal than space 0 therefore space space space space space space 0 space less or equal than space open vertical bar straight k space straight a with rightwards arrow on top close vertical bar space less or equal than space 12.$

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Classify the following measures as scalars and vectors.
(i) 5 seconds
(ii) 1000 cm³(iii) 10 Newton
(iv) 30 km hr
(v) 10 g/cm³(vi) 20 m/s towards north

(i) Time-scalar
(ii) Volume-scalar
(iii) Force-vector
(iv) Speed-scalar
(v) Density-scalar
(iv) Velocity-vector

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Represent graphically a displacement of 40 km. 30° cast of north.

The vector

OP with rightwards arrow on top

represents the required displacement.

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In given figure which of the vectors are:

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

(i) Collinear vectors : $straight a with rightwards arrow on top. space straight c with rightwards arrow on top space and space straight d with rightwards arrow on top$
(ii) Equal vectors: $straight a with rightwards arrow on top space and space straight c with rightwards arrow on top.$
(iii) Coinitial vectors: $straight b with rightwards arrow on top. space straight c with rightwards arrow on top space and space straight d with rightwards arrow on top$

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Vector Algebra

Represent graphically a displacement of 40 km. 30° cast of north.