are two vectors such that  find the angle between  from Ma

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 Multiple Choice QuestionsShort Answer Type

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151. 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 2 comma space space space open vertical bar straight b with rightwards arrow on top close vertical bar space equals space 3 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.


We have 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 3 comma space space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space 3
Let straight theta be the angle between straight a with rightwards arrow on top space and space straight b with rightwards arrow on top.
therefore space space space straight a with rightwards arrow on top. space straight b with rightwards arrow on top 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 cos space straight theta space space space space space rightwards double arrow space space space 3 space equals space left parenthesis 2 right parenthesis thin space left parenthesis 3 right parenthesis space cos space straight theta
therefore space space space space cos space straight theta space equals space 1 half space space space space space rightwards double arrow space space space space straight theta space equals space 60 degree

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152.

Find the angle between two vectors straight a with rightwards arrow on top space and space straight b with rightwards arrow on top having the same length (magnitude) square root of 2 and their scalar products is -1.

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153.

Find the angle between two vectors straight a with rightwards arrow on top space and space straight b with rightwards arrow on top such that open vertical bar straight a with rightwards arrow on top close vertical bar space equals space open vertical bar straight b with rightwards arrow on top close vertical bar space equals space 3 and straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space 1.

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154. Find the magnitude of two vectors straight a with rightwards arrow on top space and space straight b with rightwards arrow on top having the same magnitude and such that the angle between them is 30° and their scalar product is 3.
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155. Find the magnitude of two vectors straight a with rightwards arrow on top space and space straight b with rightwards arrow on top having the same magnitude and such that the angle between then is 60° and their scalar product is 1/2.
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156.

Find open vertical bar straight a with rightwards arrow on top close vertical bar and open vertical bar straight b with rightwards arrow on top close vertical bar comma if  open parentheses straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top close parentheses. space left parenthesis straight a with rightwards arrow on top space minus straight b with rightwards arrow on top right parenthesis space equals space 12 space and space open vertical bar straight a with rightwards arrow on top close vertical bar space equals 2 space open vertical bar straight b with rightwards arrow on top close vertical bar.

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157.

Find open vertical bar straight a with rightwards arrow on top close vertical bar space and space space open vertical bar straight b with rightwards arrow on top close vertical bar space if 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 space straight b with rightwards arrow on top right parenthesis space equals space 8 space space and space open vertical bar straight a with rightwards arrow on top close vertical bar space equals space 8 space open vertical bar straight b with rightwards arrow on top close vertical bar.

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158.

Find open vertical bar straight a with rightwards arrow on top close vertical bar space and space open vertical bar straight b with rightwards arrow on top close vertical bar space if space space left parenthesis straight a with rightwards arrow on top plus straight b with rightwards arrow on top right parenthesis. thin space left parenthesis straight a with rightwards arrow on top minus straight b with rightwards arrow on top right parenthesis space equals 3 space and space 2 space open vertical bar straight b with rightwards arrow on top close vertical bar space equals open vertical bar straight a with rightwards arrow on top close vertical bar.

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159.

If 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 minus straight b with rightwards arrow on top right parenthesis space equals 0 show that open vertical bar straight a with rightwards arrow on top close vertical bar space equals open vertical bar straight b with rightwards arrow on top close vertical bar

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160.

If straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space straight a with rightwards arrow on top. space straight c with rightwards arrow on top comma spaceprove that either straight a with rightwards arrow on top space equals space 0 with rightwards arrow on top or straight b with rightwards arrow on top space equals space straight c with rightwards arrow on top  or  straight a with rightwards arrow on top  is perpendicular to straight b with rightwards arrow on top minus straight c with rightwards arrow on top.

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