SATHEE: Vectors 5 Question 8

Vectors 5 Question 8

8. If $\vec{A} = (1, 1, 1), \vec{C} = (0, 1, - 1)$ are given vectors, then a vector $\vec{B}$ satisfying the equations $\vec{A} \times \vec{B} = \vec{C}$ and $\vec{A} \cdot \vec{B} = 3$ is ….

(1985,91, 2M)

Show Answer

Answer:

Correct Answer: 8. $(\frac{5}{3} \hat{i}, \frac{2}{3} \hat{j}, \frac{2}{3} \hat{k})$

Solution:

$\vec{B} = x \hat{i} + y \hat{j} + z \hat{k}$

Given, $\vec{A} = \hat{i} + \hat{j} + \hat{k}, \vec{C} = \hat{j} - \hat{k}$

Also, given $\vec{A} \times \vec{B} = \vec{C}$

$\Rightarrow (z - y) \hat{i} - (z - x) \hat{j} + (y - x) \hat{k} = \hat{j} - \hat{k}$

$\Rightarrow z - y = 0, x - z = 1, y - x = - 1$

Also, $\vec{A} \cdot \vec{B} = 3 \Rightarrow x + y + z = 3$

On solving above equations, we get

$\begin{aligned} x & = \frac{5}{3}, y = z = \frac{2}{3} \\ ∴ & \vec{B} & = (\frac{5}{3} \hat{i}, \frac{2}{3} \hat{j}, \frac{2}{3} \hat{k}) \end{aligned}$

Vectors 5 Question 8

8. If $\vec{A} = (1, 1, 1), \vec{C} = (0, 1, - 1)$ are given vectors, then a vector $\vec{B}$ satisfying the equations $\vec{A} \times \vec{B} = \vec{C}$ and $\vec{A} \cdot \vec{B} = 3$ is ….

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Vectors 5 Question 8

8. If A→=(1,1,1),C→=(0,1,−1) are given vectors, then a vector B→ satisfying the equations A→×B→=C→ and A→⋅B→=3 is ….

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu

8. If $\vec{A} = (1, 1, 1), \vec{C} = (0, 1, - 1)$ are given vectors, then a vector $\vec{B}$ satisfying the equations $\vec{A} \times \vec{B} = \vec{C}$ and $\vec{A} \cdot \vec{B} = 3$ is ….