If  from Mathematics Vector Algebra

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 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.


Here 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 4
Also,  straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space 16
therefore space space space open vertical bar straight a with rightwards arrow on top close vertical bar space open vertical bar straight b with rightwards arrow on top close vertical bar space cos space straight theta space equals space 16 space where space straight theta space is space angle space between space straight a with rightwards arrow on top space and space straight b with rightwards arrow on top.
therefore space space space left parenthesis 5 right parenthesis thin space left parenthesis 4 right parenthesis space cos space straight theta space equals space 16 space space space space space rightwards double arrow space space space space cos space straight theta space equals space 16 over 20 space equals space 4 over 5
rightwards double arrow space space space space space space space space space space space space space space space space space space space space space space space space sin space straight theta space equals space 3 over 5
therefore space space 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 open vertical bar straight a with rightwards arrow on top close vertical bar space open vertical bar straight b with rightwards arrow on top close vertical bar space sin space straight theta space equals space left parenthesis 5 right parenthesis thin space left parenthesis 4 right parenthesis space open parentheses 3 over 5 close parentheses space equals space 12

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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

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
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