Question

The area of a parallelogram whose diagonals are P= 2î +3j and Q= i +4j is

Answer 1

Answer:

Explanation:

The magnitude (length) of p is 13−−√ and the magnitude of q is 17−−√.

With the height shown the area is A=17−−√h

To find the value of h, the sine of θ and the magnitude of p can be used. Need to find the value of θ.

cosθ=p⃗ ⋅q⃗ ∥∥p⃗ ∥∥∥∥q⃗ ∥∥

cosθ=2(1)+3(4)13√17√

θ=cos−1(14221√)≈19.6538∘

sinθ=h13√

h=13−−√sinθ=13−−√sin(19.6538∘)

Substitution results in:

A=17−−√13−−√sin(19.6538∘)≈4.9999

The area of the parallelogram is 4.9999 units squared.

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