Question

if d1 vector and d2 vector are diagonal vecotrs of a parallelogram then prove that area of parallelogram is 1/2 of magnitude of d1 vector and d2 vector

Answer 1

Given vectors are,

d1→=3 i^-2 j^+4 k^ and d2→=-5 i^+2 j^-k^
Therefore, the vector and its magnitude for the asked are,

d1→=3 i^-2 j^+4 k^ and d2→=-5 i^+2 j^-k^Vector d1→+d2→=3 i^-2 j^+4 k^+-5 i^+2 j^-k^⇒d1→+d2→=-2 i^+3 k^So, its magnitude is,⇒d1→+d2→=-22+32=4+9=13⇒d1→+d2→=3.61 unitsThe vectord1→+4d2→=3 i^-2 j^+4 k^+4-5 i^+2 j^-k^⇒d1→+4d2→=-17 i^+6 j^⇒d1→+4d2→=-172+62=289+36=325⇒d1→+4d2→=18.03 units

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