In a regular hexagon `ABCDEF, bar(AB) + bar(AC)+bar(AD)+ bar(AE) + bar(AF)=k bar(AD)` then k is equal to

In a regular hexagon ABCDEF, prove that vec(AB)+vec(AC)+vec(AD)+vec(AE)+vec(AF)=3vec(AD)

In the figure shown below , bar(BC) and bar(EF) are parallel and bar(AE ) = bar(FD ) . if angle ABC is 130 ^(@) and angle (BAE) is 22^@ , what is the measure of angle (AEF) ?

In the figure shown below, E and G lie on bar(AC) , D and F lie on bar(AB), bar(DE) and bar(FG) are parallel to bar(BC) , and the given lengths are in feet. What is the length of bar(AC) , in feet?

Let bar a,bar b,bar c be three non-coplanar vectors and bar d be a non-zero vector, which is perpendicularto bar a+bar b+bar c . Now, if bar d= (sin x)(bar a xx bar b) + (cos y)(bar b xx bar c) + 2(bar c xx bar a) then minimum value of x^2+y^2 is equal to

In the figure below, A, D, C and E are collinear . bar(AD), bar(BD), and bar(BC) are all the same length, and the angle measure of /_ABD is as marked. What is the degree measure of /_BCE ?

In /_\ACD below, B is on bar(AC) , E is on bar(AD) , the measure of /_CAD is 28^(@) , and bar(AD) is perpendicular to both bar(BE) and bar(CD) . What is the measure of /_CBE ?

(bar(a)*bar(i))^(2)+(bar(a)*bar(j))^(2)+(bar(a)*bar(k))^(2)=