A force F applied on a body is written as F = | vedclass

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

Question

(D) Given the expression $F = (\hat{n} \cdot F) \hat{n} + G$,we can isolate $G$ as $G = F - (\hat{n} \cdot F) \hat{n}$.Using the vector triple product

Vedclass · Accepted Answer

$(\hat{n} 	imes F) 	imes \hat{n}$

Vedclass · Answer

(D) Given the expression $F = (\hat{n} \cdot F) \hat{n} + G$,we can isolate $G$ as $G = F - (\hat{n} \cdot F) \hat{n}$.Using the vector triple product identity $A 	imes (B 	imes C) = B(A \cdot C) - C(A \cdot B)$,we evaluate $(\hat{n} 	imes F) 	imes \hat{n}$.Note that $(\hat{n} 	imes F) 	imes \hat{n} = -\hat{n} 	imes (\hat{n} 	imes F)$.Applying the identity: $-\hat{n} 	imes (\hat{n} 	imes F) = -[\hat{n}(\hat{n} \cdot F) - F(\hat{n} \cdot \hat{n})]$.Since $\hat{n}$ is a unit vector,$\hat{n} \cdot \hat{n} = 1$.Thus,$-\hat{n}(\hat{n} \cdot F) + F(1) = F - (\hat{n} \cdot F) \hat{n}$.Comparing this with our expression for $G$,we find $G = (\hat{n} 	imes F) 	imes \hat{n}$.

$A$ force $F$ applied on a body is written as $F = (\hat{n} \cdot F) \hat{n} + G$,where $\hat{n}$ is a unit vector. The vector $G$ is equal to

Similar Questions

The angle between the vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is $\theta$. The value of the triple product $\overrightarrow{A} \cdot (\overrightarrow{B} \times \overrightarrow{A})$ is

If $|A|=2, |B|=5$ and $|A \times B|=8$. If the angle between $A$ and $B$ is acute,then $A \cdot B$ is

Two vectors $\vec{A} = 3\hat{i} + \hat{j}$ and $\vec{B} = \hat{j} + 2\hat{k}$ are given. Find the component of $\vec{A}$ along $\vec{B}$ in vector form.

Explain the meaning of multiplication of vectors by real numbers with an example.

If $\vec{A}$ and $\vec{B}$ are vectors,which of the following statements is incorrect?

Vedclass Test Series

Exam Paper Generator

Online Exam Module