If the area of the parallelogram with bar{a} | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The area of a parallelogram with adjacent sides $\bar{a}$ and $\bar{b}$ is given by $|\bar{a} 	imes \bar{b}| = 20$. We need to find the area of t

Vedclass · Accepted Answer

$140$

Vedclass · Answer

(D) The area of a parallelogram with adjacent sides $\bar{a}$ and $\bar{b}$ is given by $|\bar{a} 	imes \bar{b}| = 20$. We need to find the area of the parallelogram with adjacent sides $(3 \bar{a} + \bar{b})$ and $(2 \bar{a} + 3 \bar{b})$. The area is given by the magnitude of the cross product of these two vectors: $|(3 \bar{a} + \bar{b}) 	imes (2 \bar{a} + 3 \bar{b})|$ $= |3 \bar{a} 	imes 2 \bar{a} + 3 \bar{a} 	imes 3 \bar{b} + \bar{b} 	imes 2 \bar{a} + \bar{b} 	imes 3 \bar{b}|$ Since $\bar{a} 	imes \bar{a} = 0$ and $\bar{b} 	imes \bar{b} = 0$,and $\bar{b} 	imes \bar{a} = -(\bar{a} 	imes \bar{b})$,we have: $= |0 + 9(\bar{a} 	imes \bar{b}) - 2(\bar{a} 	imes \bar{b}) + 0|$ $= |7(\bar{a} 	imes \bar{b})| = 7 |\bar{a} 	imes \bar{b}|$ Substituting the given value $|\bar{a} 	imes \bar{b}| = 20$: Area $= 7 	imes 20 = 140$ square units.

If the area of the parallelogram with $\bar{a}$ and $\bar{b}$ as two adjacent sides is $20$ square units,then the area of the parallelogram having $3 \bar{a} + \bar{b}$ and $2 \bar{a} + 3 \bar{b}$ as two adjacent sides in square units is

Similar Questions

If $\vec{a}=\hat{i}+2 \hat{j}+\hat{k}$, $\vec{b}=3(\hat{i}-\hat{j}+\hat{k})$ and $\vec{c}$ is a vector such that $\vec{a} \times \vec{c}=\vec{b}$ and $\vec{a} \cdot \vec{c}=3$, then $\vec{a} \cdot(\vec{c} \times \vec{b}-\vec{b}-\vec{c})=$

Using vectors,prove that parallelograms on the same base and between the same parallels are equal in area.

The unit vectors perpendicular to the plane determined by the points $A(1, -1, 2)$,$B(2, 0, -1)$,and $C(0, 2, 1)$ are:

$A$ unit vector perpendicular to both $i+j+k$ and $2i+j+3k$ is

If $a, b$ and $c$ are unit vectors such that $a+b+c=0$ and the angle between $a$ and $b$ is $\frac{\pi}{3}$, then $|a \times b|+|b \times c|+|c \times a|=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module