If hati- hatj+2 hatk,2 hati+ hatj- hatk and 3 hati- hatj+2 hatk are position vectors of vertices of a triangle, if its area is √k square units then find k .

Question

If hati- hatj+2 hatk,2 hati+ hatj- hatk and 3 hati- hatj+2 hatk are position vectors of vertices of a triangle, if its area is √k square units then find k . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-ep0v05yynocdqa9b.jpg" /> Let O A= hati- hatj+2 hatk,O B=2 hati+ hatj- hatk and O C =3 hati- hatj+2 hatk are position vectors of vertices of a triangle. A B=O B-O A= hati+2 hatj-3 hatk A C=O C-O A=2 hati Area =(1/2)|A B × A C| =√13

Q. If i^−j^​+2k^,2i^+j^​−k^ and 3i^−j^​+2k^ are position vectors of vertices of a triangle, if its area is k​ square units then find k .

Let OA=i^−j^​+2k^,OB=2i^+j^​−k^ and OC=3i^−j^​+2k^ are position vectors of vertices of a triangle. AB=OB−OA=i^+2j^​−3k^ AC=OC−OA=2i^ Area =21​∣∣​AB×AC∣∣​ =13​

Q. If $\hat{i} - \hat{j} + 2 \hat{k}, 2 \hat{i} + \hat{j} - \hat{k}$ and $3 \hat{i} - \hat{j} + 2 \hat{k}$ are position vectors of vertices of a triangle, if its area is $k$ square units then find $k$ .