If  find the value of  so that  is perpendicular to . fr

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 Multiple Choice QuestionsShort Answer Type

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141.

If straight a with rightwards arrow on top space equals space 3 straight i with hat on top space plus space 2 straight j with hat on top space plus space 9 straight k with hat on top space and space straight b with rightwards arrow on top space equals space straight i with hat on top space plus space straight lambda straight j with hat on top space plus space 3 straight k with hat on top comma find the value of straight lambda so that straight a with rightwards arrow on top plus straight b with rightwards arrow on top is perpendicular to straight a with rightwards arrow on top minus straight b with rightwards arrow on top.


          straight a with rightwards arrow on top space equals space 3 straight i with hat on top space plus space 2 straight j with hat on top space plus space 9 straight k with hat on top comma space space space space straight b with rightwards arrow on top space equals space straight i with hat on top space plus space straight lambda straight j with hat on top space plus space 3 straight k with hat on top
therefore space space space straight a with rightwards arrow on top plus straight b with rightwards arrow on top space equals space 4 straight i with hat on top plus left parenthesis straight lambda plus 2 right parenthesis space straight j with hat on top plus 12 straight k with hat on top comma space space straight a with rightwards arrow on top minus straight b with rightwards arrow on top space equals space 2 space straight i with hat on top plus space left parenthesis 2 minus space straight lambda right parenthesis space straight j with hat on top space plus space 6 straight k with hat on top space
Since straight a with rightwards arrow on top plus straight b with rightwards arrow on top is perpendicular to straight a with rightwards arrow on top minus straight b with rightwards arrow on top
therefore space space space space space space space space space space space space left parenthesis straight a with rightwards arrow on top plus straight b with rightwards arrow on top right parenthesis. space left parenthesis straight a with rightwards arrow on top space minus straight b with rightwards arrow on top right parenthesis space equals space 0
therefore space space space space space space left parenthesis 4 right parenthesis thin space left parenthesis 2 right parenthesis space plus space left parenthesis straight lambda plus 2 right parenthesis thin space left parenthesis 2 minus straight lambda right parenthesis space plus space left parenthesis 12 right parenthesis thin space left parenthesis 6 right parenthesis equals space 0
therefore space space space space 8 plus 4 minus straight lambda squared plus 72 space equals 0 space space space rightwards double arrow space space space space straight lambda squared space equals space 84 space space space space rightwards double arrow space space space straight lambda space equals space plus-or-minus square root of 84 space equals plus-or-minus square root of 4 cross times 21 end root
therefore space space space space space space space straight lambda space equals plus-or-minus 2 square root of 21

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142.

Let straight a with rightwards arrow on top space equals space 5 straight i with hat on top space minus space straight j with hat on top space plus space 7 straight k with hat on top and straight b with rightwards arrow on top space equals straight i with hat on top minus straight j with hat on top plus straight lambda straight k with hat on top. Find straight lambda such that straight a with rightwards arrow on top plus straight b with rightwards arrow on top and straight a with rightwards arrow on top minus straight b with rightwards arrow on top are orthogonal .

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143.

Find straight lambda if the vectors 5 straight i with hat on top plus 2 straight j with hat on top minus straight k with hat on top and straight lambda straight i with hat on top space minus space straight j with hat on top space plus space 5 space straight k with hat on top are orthogonal.

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144.

If straight a with rightwards arrow on top space equals space 2 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 negative straight i with hat on top space plus space 2 space straight j with hat on top space plus space straight k with hat on top space space and space straight c with rightwards arrow on top space equals 3 straight i with hat on top space plus space straight j with hat on top such that straight a with rightwards arrow on top space plus space straight lambda straight b with rightwards arrow on top is perpendicular to straight c with rightwards arrow on top, then find the value of straight lambda.

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 Multiple Choice QuestionsLong Answer Type

145. Find the value of A such that the vectors 3 straight a with rightwards arrow on top plus space 4 straight b with rightwards arrow on top and 2 straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top are perpendicular to each other when 

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 Multiple Choice QuestionsShort Answer Type

146.

If open vertical bar straight a with rightwards arrow on top close vertical bar space equals space square root of 3 comma space space open vertical bar straight b with rightwards arrow on top close vertical bar space equals space 2 space and space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space 3 comma 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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147. Find the angle between two vectors straight a with rightwards arrow on top space and space straight b with rightwards arrow on top with magnitude 1 and 2 respectively and such that straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space 1
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148.

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 4 comma space space open vertical bar straight b with rightwards arrow on top close vertical bar space equals space 3 space space and space straight a with rightwards arrow on top comma space straight b with rightwards arrow on top space equals space 6 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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149.

Find the angle between two vectors straight a with rightwards arrow on top space and space straight b with rightwards arrow on top with magnitudes 2  and 1 respectively, and such that straight a with rightwards arrow on top space. space straight b with rightwards arrow on top space equals space square root of 3.

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150.

Find the angle between two vectors straight a with rightwards arrow on top space and space straight b with rightwards arrow on top with magnitudes square root of 3 space and space 2 comma space respectively comma space and space that space space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space square root of 6.

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