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Find the area of the parallelogram whose...

Find the area of the parallelogram whose diagonals are represented by the vectors
(i)`vec(d)_(1)= 3 hat(i) + hat(j) - 2 hat(k)` and `vec(d)_(2) = hat(i) - 3 hat(j) +4 hat(k)`
(ii) `vec(d)_(1)= 2 hat(i) - hat(j) + hat(k)` and `vec(d)_(2)= 3 hat(i) + 4 hat(j)-hat(k)`
(iii) `vec(d)_(1)= hat(i)- 3 hat(j) + 2 hat(k)` and `vec(d)_(2)= -hat(i)+2 hat(j).`

Text Solution

Verified by Experts

The correct Answer is:
(i) `5 sqrt(3)` sq units (ii) `1/2 sqrt(155)` sq units (iii)`1/2sqrt(21)` sq units
Area of a ||gm`=1/2|vec(d)_(1) xxvec(d)_(2)|.`
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Find the area of the parallelogram whose diagonals are represented by the vectors vec(d)_(1)=(2 hat(i) - hat(j)+ hat(k)) and vec(d)_(2) = (3 hat(i) + 4 hat(j) - hat(k)).

Find the area of the parallelogram whose adjacent sides are represented by the vectors (i) vec(a)=hat(i) + 2 hat(j)+ 3 hat(k) and vec(b)=-3 hat(i)- 2 hat(j) + hat(k) (ii) vec(a)=(3 hat(i)+hat(j) + 4 hat(k)) and vec(b)= ( hat(i)- hat(j) + hat(k)) (iii) vec(a) = 2 hat(i)+ hat(j) +3 hat(k) and vec(b)= hat(i)-hat(j) (iv) vec(b)= 2 hat(i) and vec(b) = 3 hat(j).

Knowledge Check

  • Vector vec(A)=hat(i)+hat(j)-2hat(k) and vec(B)=3hat(i)+3hat(j)-6hat(k) are :

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