Find  if for a unit vector  from Mathematics Vector Algebra

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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


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
rightwards double arrow space space open vertical bar straight x with rightwards arrow on top close vertical bar squared space minus space open vertical bar straight a with rightwards arrow on top close vertical bar squared space equals space 12
rightwards double arrow space open vertical bar straight x with rightwards arrow on top close vertical bar squared space minus space left parenthesis 1 right parenthesis squared space equals space 12 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets because space space open vertical bar straight a with rightwards arrow on top close vertical bar space equals space 1 close square brackets
rightwards double arrow space space open vertical bar straight x with rightwards arrow on top close vertical bar squared space equals space 13 space space space space space space space space space space space space space rightwards double arrow space space space open vertical bar straight x with rightwards arrow on top close vertical bar space equals square root of 13
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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.

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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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