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Solved Problems-1

  1. Two vectors are represented by Description: 83843.png. Find the dot and cross products and the angle between the vectors. Show that Description: 83834.png is at right angles to Description: 83827.png.
  2. If Description: 83819.png, find Description: 83810.png at the point (1, -2, -1).
  1. Description: 83800.png
     Description: 83792.png
    ∴  Description: 83784.png

    Now, Description: 83777.png
    Description: 83769.png
    For Description: 83761.png to be at right angles to Description: 83752.pngDescription: 83742.png should be zero.
    Description: 83735.png (Proved)
  1. Description: 83727.png
    Description: 83716.png
    At the point (1, -2, -1), the gradient is given as,
    Description: 83706.png 

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