Let vec{a} and vec{b} be two non-collinear ve | vedclass

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

Question

(B) Given the equation $2\vec{u} - \vec{v} = \vec{w}$.Substituting the expressions for $\vec{u}$,$\vec{v}$,and $\vec{w}$:$2(x\vec{a} + 2y\vec{b}) - (-

Vedclass · Accepted Answer

$x = 10/7, y = 4/7$

Vedclass · Answer

(B) Given the equation $2\vec{u} - \vec{v} = \vec{w}$.Substituting the expressions for $\vec{u}$,$\vec{v}$,and $\vec{w}$:$2(x\vec{a} + 2y\vec{b}) - (-2y\vec{a} + 3x\vec{b}) = 4\vec{a} - 2\vec{b}$$(2x\vec{a} + 4y\vec{b}) + (2y\vec{a} - 3x\vec{b}) = 4\vec{a} - 2\vec{b}$$(2x + 2y)\vec{a} + (4y - 3x)\vec{b} = 4\vec{a} - 2\vec{b}$Since $\vec{a}$ and $\vec{b}$ are non-collinear,we can equate the coefficients:$2x + 2y = 4 \Rightarrow x + y = 2$ (Equation $1$)$-3x + 4y = -2$ (Equation $2$)From Equation $1$,$x = 2 - y$. Substituting into Equation $2$:$-3(2 - y) + 4y = -2$$-6 + 3y + 4y = -2$$7y = 4 \Rightarrow y = 4/7$Substituting $y = 4/7$ into $x = 2 - y$:$x = 2 - 4/7 = 10/7$Thus,$x = 10/7$ and $y = 4/7$.

Let $\vec{a}$ and $\vec{b}$ be two non-collinear vectors. For what values of $x$ and $y$ is the equation $2\vec{u} - \vec{v} = \vec{w}$ true,where $\vec{u} = x\vec{a} + 2y\vec{b}$,$\vec{v} = -2y\vec{a} + 3x\vec{b}$,and $\vec{w} = 4\vec{a} - 2\vec{b}$?

Similar Questions

$A$ and $B$ are two points. The position vector of $A$ is $6b - 2a$. $A$ point $P$ divides the line segment $AB$ in the ratio $1 : 2$. If $a - b$ is the position vector of $P$,then the position vector of $B$ is given by:

The position vectors of four points $P, Q, R, S$ are $2a + 4c$,$5a + 3\sqrt{3}b + 4c$,$-2\sqrt{3}b + c$,and $2a + c$ respectively. Then:

The number of values of $m \in R$ for which the vectors $\hat{i}+2 \hat{j}+m \hat{k}$ and $\hat{i}+m \hat{j}+2 \hat{k}$ are collinear is

If $3 \hat{i}-5 \hat{j}+2 \hat{k}, 7 \hat{i}+2 \hat{j}-4 \hat{k}, \hat{i}-3 \hat{j}+4 \hat{k}$ and $-7 \hat{i}-17 \hat{j}+16 \hat{k}$ are position vectors of the points $A, B, C$ and $D$ respectively, then the angle between $\overrightarrow{AB}$ and $\overrightarrow{CD}$ is

Let $\vec{v}$ be a vector in the plane such that $|\vec{v} - \hat{i}| = |\vec{v} - 2\hat{j}| = |\vec{v} - \hat{j}|$. Then,$|\vec{v}|$ lies in the interval

Vedclass Test Series

Exam Paper Generator

Online Exam Module