Area of a rectangle having vertices A,B,C and D with position vectors - i + 2 j + 4 k, , , , i + 2 j + 4 k, , , , i - 2 j + 4 k and - i - 2 j + 4 k respectively is 2 1 2 4

Correct Option is c Here, = ( i + 2 j + 4 k) - ( - i + 2 j + 4 k) = 2 i | | = 2 and = ( - i - 2 j + 4 k) - ( - i + 2 j + 4 k) = - j | | = 1 Area of rectangle Miscellaneous Exercise

Vector Algebra — Class 12 Maths Solution

ncert exercise SA NCERT,Page 454,Ex.10.4,Q.No 12

Question

Area of a rectangle having vertices $A,B,C$ and $D$ with position vectors
$- \hat i + \cfrac{1}{2}\hat j + 4\hat k,\,\,\,\hat i + \cfrac{1}{2}\hat j + 4\hat k,\,\,\,\hat i - \cfrac{1}{2}\hat j + 4\hat k$ and $- \hat i - \cfrac{1}{2}\hat j + 4\hat k$ respectively is

• $\cfrac{1}{2}$

• $1$

• $2$

• $4$

Step-by-step Solution

{Correct Option is c}

Here, $\overrightarrow {AB} = (\hat i + \cfrac{1}{2}\hat j + 4\hat k) - ( - \hat i + \cfrac{1}{2}\hat j + 4\hat k) = 2\hat i$
$\Rightarrow |\overrightarrow {AB} | = 2$

and $\overrightarrow {AD} = ( - \hat i - \cfrac{1}{2}\hat j + 4\hat k) - ( - \hat i + \cfrac{1}{2}\hat j + 4\hat k) = - \hat j$

$\Rightarrow |\overrightarrow {AD} | = 1$
$\Rightarrow$ Area of rectangle

Miscellaneous Exercise

← All Vector Algebra solutions Practice tests →

NCERT & Exemplar solution for CBSE Class 12 Mathematics, Vector Algebra. Curated by Sachin Sharma. Free for all students.