The values of x and y for which vectors vec{A | vedclass

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

Question

(B) Two vectors $\vec{A} = A_x \hat{i} + A_y \hat{j} + A_z \hat{k}$ and $\vec{B} = B_x \hat{i} + B_y \hat{j} + B_z \hat{k}$ are parallel if their comp

Vedclass · Accepted Answer

$x = \frac{36}{5}, y = \frac{5}{3}$

Vedclass · Answer

(B) Two vectors $\vec{A} = A_x \hat{i} + A_y \hat{j} + A_z \hat{k}$ and $\vec{B} = B_x \hat{i} + B_y \hat{j} + B_z \hat{k}$ are parallel if their components are proportional,i.e.,$\frac{A_x}{B_x} = \frac{A_y}{B_y} = \frac{A_z}{B_z}$.Given $\vec{A} = 6 \hat{i} + x \hat{j} - 2 \hat{k}$ and $\vec{B} = 5 \hat{i} + 6 \hat{j} - y \hat{k}$.Equating the ratios: $\frac{6}{5} = \frac{x}{6} = \frac{-2}{-y}$.First,solve for $x$: $\frac{6}{5} = \frac{x}{6} \implies x = \frac{6 	imes 6}{5} = \frac{36}{5}$.Next,solve for $y$: $\frac{6}{5} = \frac{-2}{-y} \implies \frac{6}{5} = \frac{2}{y} \implies 6y = 10 \implies y = \frac{10}{6} = \frac{5}{3}$.Thus,the values are $x = \frac{36}{5}$ and $y = \frac{5}{3}$.

The values of $x$ and $y$ for which vectors $\vec{A} = (6 \hat{i} + x \hat{j} - 2 \hat{k})$ and $\vec{B} = (5 \hat{i} + 6 \hat{j} - y \hat{k})$ are parallel are

Similar Questions

Find the unit vector of a vector whose coordinates are $(8, 6)$.

Can you associate vectors with $(a)$ the length of a wire bent into a loop,$(b)$ a plane area,$(c)$ a sphere? Explain.

Which of the following colours has the highest energy if the wavelengths of violet, blue, yellow, and red light are $410 \text{ nm}$, $470 \text{ nm}$, $580 \text{ nm}$, and $750 \text{ nm}$ respectively?

Which of the following is not a vector quantity?

The resultant magnitude of two vectors of same magnitude is equal to the magnitude of either. The angle between the two vectors is (in $^{\circ}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module