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Show that the area of a parallelogram wi...

Show that the area of a parallelogram with diagonals `veca` and `vecb` is `1/2|veca xx vecb|`

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Consider the vectors veca=hati-hatj+3hatk and vecb=3hati-7hatj+hatk Find the area of the parallelogram with adjacent sides veca and vecb .

Consider the vectors veca=i-7j+7k,vecb=3i-2j+2k . Find the area of parallelogram with adjacent sides veca and vecb .

Knowledge Check

  • If vecA=hati+2hatj+3hatk and vecB=3hati-2hatj then the area of the parallelogram formied from these vectors as adjacent sides will be

    A
    `2 sqrt(3)` square units
    B
    `4 sqrt(3)` square units
    C
    `6 sqrt(3)` square units
    D
    `8sqrt(3)` square units

  • If theta is the angle between any two vectors veca and vecb , then |veca.vecb|=|veca xx vecb| when theta is equal to a)0 b) pi/4 c) pi/2 d) pi

    A
    0
    B
    pi/4'
    C
    pi/2'
    D
    pi'

  • If theta is the acute angle between any two vectors " " veca" and "vecb , then |veca.vecb|=|vecaxxvecb| when theta is equal to :

    A
    0
    B
    `pi/4`
    C
    `pi/2`
    D
    `pi`

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    Let veca=2hati-4hatj+5hatk and vecb=hati-2hatj-8hatk be two vectors Find a vector vecc representing a diagonal of the parallelogram with veca and vecb as the adjacent sides.

    If veca,vecb,vecc,vecd respectively are the position vectors representing the vertices A,B,C,D of a parallelogram, then write vecd in terms of veca,vecb,vecc .

    Show that (veca-vecb) xx(veca+vecb)=2(veca xx vecb)

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    If |veca| =2 , vecb =2 hati - hatj -3hatk and the angel between veca and vecb is (pi)/(4) then veca.vecb is equal to

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