If overrightarrow{a}=hat{i}-hat{j}-hat{k} and | vedclass

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

Question

(B) The formula for the orthogonal projection of vector $\overrightarrow{b}$ on vector $\overrightarrow{a}$ is given by $\frac{(\overrightarrow{b} \cd

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) The formula for the orthogonal projection of vector $\overrightarrow{b}$ on vector $\overrightarrow{a}$ is given by $\frac{(\overrightarrow{b} \cdot \overrightarrow{a}) \overrightarrow{a}}{|\overrightarrow{a}|^2}$.Given that the projection is $\frac{4}{3}(\hat{i}-\hat{j}-\hat{k})$, we have:$\frac{(\overrightarrow{b} \cdot \overrightarrow{a}) \overrightarrow{a}}{|\overrightarrow{a}|^2} = \frac{4}{3}(\hat{i}-\hat{j}-\hat{k})$First, calculate $\overrightarrow{b} \cdot \overrightarrow{a}$:$\overrightarrow{b} \cdot \overrightarrow{a} = (\lambda \hat{i}-3 \hat{j}+\hat{k}) \cdot (\hat{i}-\hat{j}-\hat{k}) = \lambda(1) + (-3)(-1) + (1)(-1) = \lambda + 3 - 1 = \lambda + 2$.Next, calculate $|\overrightarrow{a}|^2$:$|\overrightarrow{a}|^2 = (1)^2 + (-1)^2 + (-1)^2 = 1 + 1 + 1 = 3$.Substituting these into the projection formula:$\frac{(\lambda + 2)(\hat{i}-\hat{j}-\hat{k})}{3} = \frac{4}{3}(\hat{i}-\hat{j}-\hat{k})$.Comparing both sides, we get:$\frac{\lambda + 2}{3} = \frac{4}{3} \Rightarrow \lambda + 2 = 4 \Rightarrow \lambda = 2$.

If $\overrightarrow{a}=\hat{i}-\hat{j}-\hat{k}$ and $\overrightarrow{b}=\lambda \hat{i}-3 \hat{j}+\hat{k}$ and the orthogonal projection of $\overrightarrow{b}$ on $\overrightarrow{a}$ is $\frac{4}{3}(\hat{i}-\hat{j}-\hat{k})$, then $\lambda$ is equal to

Similar Questions

Radius of gyration of a body depends on

The enthalpy change $(\Delta H)$ for the reaction,$N_{2(g)} + 3H_{2(g)} \longrightarrow 2NH_{3(g)}$ is $-92.38 \ kJ$ at $298 \ K$. The internal energy change $\Delta U$ at $298 \ K$ is ...... $kJ$.

What is the plant body of algae called?

$AB_{3(g)}$ dissociates as: $AB_{3(g)} \rightleftharpoons AB_{2(g)} + \frac{1}{2}B_{2(g)}$. When the initial pressure of $AB_3$ is $800 \ torr$ and the total pressure developed at equilibrium is $900 \ torr$,what percentage of $AB_{3(g)}$ is dissociated?

Which one of the following salts gives an acidic solution in water?

Vedclass Test Series

Exam Paper Generator

Online Exam Module