help@askiitians.com

+91-93193 64476

Vectors> if abcd is a quadrilateral and e & f are ...

question mark

if abcd is a quadrilateral and e & f are midpoint of ac & bd respectively. prove that ab+ac+cb+cd = 4ef

PRASHANT KUMAR , 11 Years ago

Grade 12th pass

1 Answers

Satyajit Samal

The correct question is $AB+AD+CB+CD=4EF$
Since F is the midpoint of BD, we get $AB+AD = 2AF$ …...(1)
Similarly $CB+CD = 2 CF$ …....(2)
Adding (1) and (2) we get $AB+AD+CB+CD=2\left ( AF+CF \right ) \\ \Rightarrow AB+AD+CB+CD = -2\left ( FA+FC \right ) \\ \Rightarrow AB+AD+CB+CD = -2 \left ( 2FE \right ) \\ \RIghtarrow AB+AD+CB+CD = 4EF$
Hence proved.

Last Activity: 11 Years ago

LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

Full Live Access

Study Material

Live Doubts Solving

Daily Class Assignments

A body is rotating with an angular velocity of 2radians per second about the line joining (1, 2,3) and (2, 3,5) find the velocity of the particle of the body which is momentarily at (3, 5,6)

vectors

1 Answer Available

Last Activity: 3 Years ago

Show that: vectorPQ+vectorPR+ vectorPS +vectorTP+vectorUP = 4PQ
Vector

vectors

1 Answer Available

Last Activity: 4 Years ago

Given that A×(B×C) = (A.C)B - ( A.B)C , deduce that (A×B)×C = (A.C)B - (B.C)A

vectors

1 Answer Available

Last Activity: 4 Years ago

the mean of 30 observations was 17 with sd2. later it was found that two of the observations were incorrect, which were recorded as 19vand 21.find the correct sd if the incorrect values are deleted and correct values 22 and 15 are included

vectors

1 Answer Available

Last Activity: 4 Years ago

Find the component of 2i +3j +k in the direction of 3i-j

vectors

1 Answer Available

Last Activity: 4 Years ago

View all Questions