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Vector Algebra

Short Answer Type

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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56. Find the magnitude of the vector

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

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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.

Let $straight a with rightwards arrow on top space equals space straight x space left parenthesis straight i with hat on top space plus space straight j with hat on top space plus space straight k with hat on top right parenthesis space equals space straight x space straight i with hat on top space plus space straight x space straight j with hat on top space plus space straight x space straight k with hat on top$
Since $straight a with rightwards arrow on top$ is a unit vector
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