If  then show that the vectors  from Mathematics Vector Alge

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 Multiple Choice QuestionsShort Answer Type

131. Given two points A and B, identify the set of points P in space such that PA with rightwards arrow on top. space PB with rightwards arrow on top space less than space 0.
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132.

Find open vertical bar straight x with rightwards arrow on top close vertical bar comma space if for a unit vector straight a with rightwards arrow on top comma space left parenthesis straight x with rightwards arrow on top minus straight a with rightwards arrow on top right parenthesis. space left parenthesis straight x with rightwards arrow on top plus straight a with rightwards arrow on top right parenthesis space equals space 12

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133.

If straight a with rightwards arrow on top is the unit vector and open parentheses straight x with rightwards arrow on top minus straight a with rightwards arrow on top close parentheses. space left parenthesis straight x with rightwards arrow on top space plus space straight a with rightwards arrow on top right parenthesis space equals space 8 comma then find open vertical bar straight x with rightwards arrow on top close vertical bar.

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134.

If straight a with rightwards arrow on top. space straight a with rightwards arrow on top space equals space 0 and straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space 0 comma then what can be concluded about the vector straight b with rightwards arrow on top?

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135.

If either vector straight a with rightwards arrow on top space equals space 0 with rightwards arrow on top space space or space straight b with rightwards arrow on top space equals space 0 comma space then space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space 0. But the converse need not be true. Justify your answer with an example. 

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136. Find the angle between the vectors straight i with hat on top space minus space 2 space straight j with hat on top space plus space 3 space straight k with hat on top space and space 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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137. Find the angle between vectors straight a with rightwards arrow on top plus straight b with rightwards arrow on top and straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top if 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 3 space straight k with hat on top and straight b with rightwards arrow on top space equals space 3 space straight i with hat on top space plus space straight j with hat on top space minus space 2 space straight k with hat on top
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138.

If straight a with rightwards arrow on top space equals space straight i with hat on top plus space 2 space straight j with hat on top space space minus space 3 space straight k with hat on top comma space space straight b with rightwards arrow on top space equals space 3 space straight i with hat on top space minus space straight j with hat on top space plus space 2 space straight k with hat on top comma space space show that open parentheses straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top close parentheses space and space left parenthesis straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top right parenthesis are perpendicular to each other. 

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139.

If straight a with rightwards arrow on top space equals space 5 space straight i with hat on top space minus space straight j with hat on top space minus space space 3 space 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 plus 3 space straight j with hat on top space minus space 5 space straight k with hat on top comma space then show that the vectors straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top space and space straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top space are space orthogonal.


       straight a with rightwards arrow on top space equals space 5 space straight i with hat on top space minus space straight j with hat on top space minus space 3 space straight k with hat on top comma space space straight b with rightwards arrow on top space equals space straight i with hat on top space plus space 3 space straight j with hat on top space minus space 5 space straight k with hat on top
therefore space space space space straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top space equals space 6 space straight i with hat on top space plus space 2 space straight j with hat on top space minus space 8 space straight k with hat on top comma space space straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top space equals space 4 space straight i with hat on top space minus space 4 space straight j with hat on top space plus space 2 space straight k with hat on top
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 space straight b with rightwards arrow on top right parenthesis space equals space left parenthesis 6 right parenthesis thin space left parenthesis 4 right parenthesis space plus space left parenthesis 2 right parenthesis thin space left parenthesis 4 right parenthesis space plus space left parenthesis negative 8 right parenthesis thin space left parenthesis 2 right parenthesis
                      equals space 24 minus 8 minus 16 space equals space 0
therefore space space space straight a with rightwards arrow on top plus straight b with rightwards arrow on top space and space straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top space are space orthogonal space vectors. space

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140. For what values of A are the vectors 
straight a with rightwards arrow on top space equals space 2 space straight i with hat on top space plus space straight lambda space straight j with hat on top space plus space 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 minus space 2 space straight j with hat on top space plus space 3 space straight k with hat on top perpendicular to each other?
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