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Show that the triangle formed by the vec...

Show that the triangle formed by the vectors `3bar(i)+5bar(j)+2bar(k), 2bar(i)-3bar(j)-5bar(k), -5bar(i)-2bar(j)+3bar(k)` is equilateral.

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If the triangle formed by the vectors 3 bar(i) + 5 bar(j) + 2 bar(k) , 2 bar(i) - 3 bar(j) - 5 bar(k) and - 5 bar(i) - 2 bar(j) + 3 bar(k) equilateral ?

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Find the vector area and area of the triangle with vertices bar(i) + bar(j)-bar(k), 2bar(i)- 3bar(j) + bar(k), 3 bar(i) + bar(j)- 2bar(k) .

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The points with P.V's bar(i)+2bar(j)+bar(k), 2bar(i)+3bar(j)+4bar(k) and 4bar(i)+5bar(j)+10bar(k) form