Given vectors

Question

Find a b, 2a + 3b, lal, and la-bl

Answer 1

Calculate the a+b.

a+b=(i+2j-4k)+(-3i-j+6k)

      =(1+(-3))i+(2+(-1))j+(-4+6)k

       =-2i+j+2k

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Calculate the 2a+3b.

2a+3b=2(i+2j-4k)+3(-3i-j+6k)

          =(2(1)+3(-3))i+(2(2)+3(-1))j+(2(-4)+3(6))k

         =(2-9)i+(4-3)j+(-8+18)k

          =-7i+j+10k

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Calculate the |a|.

a=(i+2j-4k)

|a|=sqrt((1)^2+(2)^2+(-4)^2)

       =sqrt(1+4+16)

       =sqrt(21)

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Calculate the a-b.

a-b=(i+2j-4k)-(-3i-j+6k)

      =(1-(-3))i+(2-(-1))j+(-4-6)k

       =4i+3j-10k

Calculate the |a-b|.

|a-b|=sqrt((4)^2+(3)^2+(-10)^2)

        =sqrt(16+9+100)

        =sqrt(125)

       =5sqrt(5)