Question

In figure, vector AB = 3 i  – j , AC = 2i  + 3 j  and DE = 4 i  – 2 j  then the area of the shaded region in square units is

(a)  15 

(b)  6

(c)  7

(d)  8

Answer 1

Correct option (c) 7

Explanation:

We have vector BC = BA + AC

= (– 3i + j ) + (2 i  + 3 j) = – i  + 4 j

Vector Area of shaded region

Area = 7sq.units

Comments

How did EB-EC come?

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vec(EC x ED) = vec(-ED x EC)
⇒ 1/2 vec(ED) x vec(EB) + 1/2 vec(EC) x vec(ED)
= 1/2 vec(ED) x vec(EB) -1/2 vec(ED) x vec(EC)
= 1/2 vec(ED) x vec(EB - EC)