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51. Find the sum of the vectors

straight a with rightwards arrow on top space equals space straight i with hat on top space minus space 2 straight j with hat on top space plus straight k with hat on top comma space space straight b with rightwards arrow on top space equals space minus 2 straight i with hat on top space plus space 4 straight j with hat on top space plus space 5 straight k with hat on top comma space straight c with rightwards arrow on top space equals space straight i with hat on top space minus space 6 straight j with hat on top space minus space 7 straight k with hat on top

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52. Compute the magnitude of the following vectors:

straight a with rightwards arrow on top space equals space straight i with hat on top space plus space straight j with hat on top space plus space straight k with hat on top space space semicolon space space space straight b with rightwards arrow on top space equals space 2 straight i with hat on top space minus space 7 straight j with hat on top space minus space 3 straight k with hat on top semicolon space space straight c with rightwards arrow on top space equals space fraction numerator 1 over denominator square root of 3 end fraction straight i with hat on top space plus space fraction numerator 1 over denominator square root of 3 end fraction straight j with hat on top space minus space fraction numerator 1 over denominator square root of 3 end fraction straight k with hat on top

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53. Write two different vectors having same magnitude.

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54. Write two different vector having same direction.

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55. Find the values of x, y and z so that the vectors

straight a with rightwards arrow on top space equals straight x space straight i with hat on top space plus space 2 space straight j with hat on top space plus space straight z space straight k with hat on top

and

straight b with rightwards arrow on top space equals space 2 space straight i with hat on top space plus space straight y space straight j with hat on top space plus space straight k with hat on top

are equal.

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straight a with rightwards arrow on top space equals space 2 space straight i with hat on top space minus space 6 space straight j with hat on top space minus space 3 space straight k with hat on top

therefore space space space space space open vertical bar straight a with rightwards arrow on top close vertical bar space equals space square root of left parenthesis 2 right parenthesis squared plus left parenthesis negative 6 right parenthesis squared plus left parenthesis negative 3 right parenthesis squared end root

equals space square root of 4 plus 36 plus 9 end root space equals space square root of 49 space equals space 7

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57. Find values of x for which

straight x space open parentheses straight i with hat on top space plus space straight j with hat on top space plus space straight k with hat on top close parentheses

is a unit vector.

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58. Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (– 5, 7).

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59. Find the vector joining the points P(2, 3, 0) and Q (– 1, – 2, – 4) directed from P to Q.

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60. Find the unit vector in the direction of vector

PQ with rightwards arrow on top

, where P and Q are the points (1, 2, 3) and (4, 5, 6) respectively.

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