Find the area of the parallelogram having two adjacent sides OA
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    Vector Algebra

    Multiple Choice QuestionsLong Answer Type

    251. Find a vector of magnitude 9 and which is perpendicular to both the vectors
    straight a with rightwards arrow on top space equals space 4 straight i with hat on top space minus space straight j with hat on top space plus space 3 space straight k with hat on top comma space space space straight b with rightwards arrow on top space equals space minus 2 space straight i with hat on top space space plus space straight j with hat on top space minus space 2 space straight k with hat on top
     
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    252. Find a vector of magnitude 19 and which is perpendicular to both the vectors 4 space straight i with hat on top space minus space straight j with hat on top space plus space 8 space straight k with hat on top comma space space space straight b with rightwards arrow on top space equals space minus straight j with hat on top space plus space straight k with hat on top
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    253. Find a vector of magnitude 5 units, perpendicular to each of the vectors
    left parenthesis straight a with rightwards arrow on top plus straight b with rightwards arrow on top right parenthesis space and space left parenthesis straight a with rightwards arrow on top space minus straight b with rightwards arrow on top right parenthesis where straight a with rightwards arrow on top space equals space straight i with hat on top plus straight j with hat on top plus straight k with hat on top and straight b with rightwards arrow on top space equals space straight i with hat on top space plus space 2 straight j with hat on top space plus 3 straight k with hat on top.
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    Multiple Choice QuestionsShort Answer Type

    254. Find the sine of the angle between the vectors
    straight a with rightwards arrow on top space equals space 2 space straight i with hat on top space minus space straight j with hat on top space plus space straight k with hat on top space space space and space straight b with rightwards arrow on top space equals space 3 space straight i with hat on top space plus space 4 space straight j with hat on top space minus space straight k with hat on top. Also find a unit vector perpendicular to both the vectors. 
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    255. Find the sine of the angle between the vectors
    straight a with rightwards arrow on top space equals space 2 space straight i with hat on top space minus space 3 space straight j with hat on top space plus space 4 space straight k with hat on top space and space straight b with rightwards arrow on top space equals 3 space straight i with hat on top space plus space 4 space straight j with hat on top space minus space 5 space straight k with hat on top
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    256.

    If straight a with rightwards arrow on top space and space straight b with rightwards arrow on top are two vectors such that open vertical bar straight a with rightwards arrow on top close vertical bar space equals space 2 comma space space space open vertical bar straight b with rightwards arrow on top close vertical bar space equals space 7 and straight a with rightwards arrow on top cross times straight b with rightwards arrow on top space equals space 3 space straight i with hat on top space plus space 2 space straight j with hat on top space plus space 6 space straight k with hat on top space semicolon find the angle between straight a with rightwards arrow on top space and space straight b with rightwards arrow on top.

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    257.

    If open vertical bar straight a with rightwards arrow on top close vertical bar space equals space 5 comma space space space open vertical bar straight b with rightwards arrow on top close vertical bar space equals space 4 space and space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space 16 comma space find space open vertical bar straight a with rightwards arrow on top cross times space straight b with rightwards arrow on top close vertical bar.

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    258.

    Find open vertical bar straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top close vertical bar if   open vertical bar straight a with rightwards arrow on top close vertical bar space equals space 10 comma space space space space space open vertical bar straight b with rightwards arrow on top close vertical bar space equals space 2 space space and space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space 12.

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    Multiple Choice QuestionsLong Answer Type

    259. Use vector method only to find the values of a and b if points (2, b, 3), (a, – 5, 1) and ( – 1, 11, 9) are collinear.
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    Multiple Choice QuestionsShort Answer Type

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    260. Find the area of the parallelogram having two adjacent sides OA and OB where O is the origin and the position vectors of A and B are respectively
    straight a with rightwards arrow on top space equals space straight i with hat on top plus 2 space straight j with hat on top space plus space 3 space straight k with hat on top and  straight b with rightwards arrow on top space equals space minus 3 space straight i with hat on top space minus space 2 space straight j with hat on top space plus space straight k with hat on top

    straight a with rightwards arrow on top space equals space straight i with hat on top space plus space 2 space straight j with hat on top space plus space 3 space straight k with hat on top comma space space space straight b with rightwards arrow on top space equals space minus 3 space straight i with hat on top space minus space 2 space straight j with hat on top space plus space straight k with hat on top
    straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top space equals space open vertical bar table row cell straight i with hat on top end cell cell straight j with hat on top end cell cell straight k with hat on top end cell row 1 2 3 row cell negative 3 end cell cell negative 2 end cell 1 end table close vertical bar space equals space left parenthesis 2 plus 6 right parenthesis space straight i with hat on top space minus space left parenthesis 1 plus 9 right parenthesis straight j with hat on top space plus space left parenthesis negative 2 plus 6 right parenthesis space straight k with hat on top space equals space 8 straight i with hat on top space minus space 10 straight j with hat on top space plus space 4 straight k with hat on top
    open vertical bar straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top close vertical bar space equals space square root of left parenthesis 8 right parenthesis squared plus left parenthesis negative 10 right parenthesis squared plus left parenthesis 4 right parenthesis squared end root space equals space square root of 180 therefore space space space area space of space vertical line vertical line space gm space equals space open vertical bar straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top close vertical bar space equals space square root of 180
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