Let vec{u} = 2hat{i} + 3hat{j} + hat{k},vec{v | vedclass

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

Question

(A) Given vectors are $\vec{u} = 2\hat{i} + 3\hat{j} + \hat{k}$,$\vec{v} = -3\hat{i} + 2\hat{j}$,and $\vec{w} = \hat{i} - \hat{j} + 4\hat{k}$.Two vect

Vedclass · Accepted Answer

$\vec{u}$ is perpendicular to $\vec{v}$ but not $\vec{w}$

Vedclass · Answer

(A) Given vectors are $\vec{u} = 2\hat{i} + 3\hat{j} + \hat{k}$,$\vec{v} = -3\hat{i} + 2\hat{j}$,and $\vec{w} = \hat{i} - \hat{j} + 4\hat{k}$.Two vectors are perpendicular if their dot product is $0$.First,calculate $\vec{u} \cdot \vec{v} = (2)(-3) + (3)(2) + (1)(0) = -6 + 6 + 0 = 0$. Since the dot product is $0$,$\vec{u} \perp \vec{v}$.Next,calculate $\vec{u} \cdot \vec{w} = (2)(1) + (3)(-1) + (1)(4) = 2 - 3 + 4 = 3 
eq 0$. Thus,$\vec{u}$ is not perpendicular to $\vec{w}$.Finally,calculate $\vec{v} \cdot \vec{w} = (-3)(1) + (2)(-1) + (0)(4) = -3 - 2 + 0 = -5 
eq 0$. Thus,$\vec{v}$ is not perpendicular to $\vec{w}$.Therefore,$\vec{u}$ is perpendicular to $\vec{v}$ but not to $\vec{w}$.

Let $\vec{u} = 2\hat{i} + 3\hat{j} + \hat{k}$,$\vec{v} = -3\hat{i} + 2\hat{j}$ and $\vec{w} = \hat{i} - \hat{j} + 4\hat{k}$. Then which of the following statements is true?

Similar Questions

The magnitude of the projection of the vector $\vec{a} = 4\hat{i} - 3\hat{j} + 2\hat{k}$ on the line which makes equal angles with the coordinate axes is

Find the angle $\theta$ between the vectors $\vec{a} = \hat{i} + \hat{j} - \hat{k}$ and $\vec{b} = \hat{i} - \hat{j} + \hat{k}$.

If $a \cdot b = 0$ and $a + b$ makes an angle $60^{\circ}$ with $a$,then

If $\theta$ is the angle between the vectors $4 \hat{i}-\hat{j}+2 \hat{k}$ and $\hat{i}+3 \hat{j}-2 \hat{k}$, then $\sin 2 \theta=$

Let $\vec{u}$ and $\vec{v}$ be two non-zero vectors with the intermediate angle $45^{\circ}$. Then $|\vec{u} \times \vec{v}|=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module