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Vector Algebra

Question
CBSEENMA12036126
Wired Faculty App

Let space straight a with rightwards arrow on top space equals space 2 straight i with hat on top space plus straight j with hat on top minus 2 straight k with hat on top space and space straight b with rightwards arrow on top space equals straight i with hat on top space plus straight j with hat on top. space Let space straight c with rightwards arrow on top space be space straight a space vector space such space that space vertical line straight c with rightwards arrow on top minus straight a with rightwards arrow on top vertical line equals 3 vertical line left parenthesis straight a with rightwards arrow on top space straight x straight b with rightwards arrow on top right parenthesis space straight x straight c with rightwards arrow on top vertical line space equals space 3 space and space the space angle space between space straight c with rightwards arrow on top space and space straight a with rightwards arrow on top space straight x space straight b with rightwards arrow on top space be space 30 to the power of straight o. space Then space straight a with rightwards arrow on top. straight c with rightwards arrow on top space is space equal space to space

  • 1/8

  • 25/8

  • 2

  • 5

Solution

C.

2

straight a with rightwards arrow on top space equals space 2 straight i with hat on top space plus straight j with hat on top minus 2 straight k with hat on top comma straight b with rightwards arrow on top space equals space straight i with hat on top space plus straight j with hat on top space and space vertical line straight a with hat on top vertical line space equals space 3 therefore comma space straight a with rightwards arrow on top space straight x straight b with rightwards arrow on top space equals space space 2 straight i with hat on top space minus 2 straight j with hat on top plus straight k with hat on top comma left parenthesis straight a with rightwards arrow on top space straight x straight b with rightwards arrow on top right parenthesis space straight x straight c with rightwards arrow on top space equals space vertical line straight a with rightwards arrow on top space straight x straight b with rightwards arrow on top vertical line vertical line straight c with rightwards arrow on top vertical line space sin space 30 space straight n with hat on top vertical line left parenthesis straight a with rightwards arrow on top space straight x space straight b with rightwards arrow on top right parenthesis space straight x space straight c with rightwards arrow on top vertical line space equals space 3. vertical line straight c with rightwards arrow on top vertical line.1 half 3 space equals space 3 vertical line straight c with rightwards arrow on top vertical line.1 half therefore space vertical line straight c with rightwards arrow on top vertical line space equals space 2 Now colon space vertical line straight c with rightwards arrow on top minus straight a with rightwards arrow on top vertical line space equals space 3 straight c squared space plus straight a squared space minus 2 straight c with rightwards arrow on top. straight a with rightwards arrow on top space equals space 9 4 space plus space 9 space minus 2 straight a with rightwards arrow on top. straight c with rightwards arrow on top space equals space 9 straight a with rightwards arrow on top. straight c with rightwards arrow on top space equals space 2

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The Boolean Expression (p∧~q)∨q∨(~p∧q) is equivalent to:

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