A vector perpendicular to hat{i}+hat{j}+hat{k | vedclass

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

Question

(D) Two vectors $\vec{A}$ and $\vec{B}$ are perpendicular if their dot product is zero,i.e.,$\vec{A} \cdot \vec{B} = 0$.Let $\vec{A} = \hat{i} + \hat{

Vedclass · Accepted Answer

$3\hat{i}+2\hat{j}-5\hat{k}$

Vedclass · Answer

(D) Two vectors $\vec{A}$ and $\vec{B}$ are perpendicular if their dot product is zero,i.e.,$\vec{A} \cdot \vec{B} = 0$.Let $\vec{A} = \hat{i} + \hat{j} + \hat{k}$.For option $A$: $(\hat{i} + \hat{j} + \hat{k}) \cdot (\hat{i} - \hat{j} + \hat{k}) = (1)(1) + (1)(-1) + (1)(1) = 1 - 1 + 1 = 1 
eq 0$.For option $B$: $(\hat{i} + \hat{j} + \hat{k}) \cdot (\hat{i} - \hat{j} - \hat{k}) = (1)(1) + (1)(-1) + (1)(-1) = 1 - 1 - 1 = -1 
eq 0$.For option $C$: $(\hat{i} + \hat{j} + \hat{k}) \cdot (-\hat{i} - \hat{j} - \hat{k}) = (1)(-1) + (1)(-1) + (1)(-1) = -1 - 1 - 1 = -3 
eq 0$.For option $D$: $(\hat{i} + \hat{j} + \hat{k}) \cdot (3\hat{i} + 2\hat{j} - 5\hat{k}) = (1)(3) + (1)(2) + (1)(-5) = 3 + 2 - 5 = 0$.Since the dot product is zero for option $D$,it is the correct answer.

$A$ vector perpendicular to $\hat{i}+\hat{j}+\hat{k}$ is:

Similar Questions

Consider a vector $\overrightarrow{F} = 4\hat{i} - 3\hat{j}$. Another vector that is perpendicular to $\overrightarrow{F}$ is

If $\vec{A}, \vec{B}$ and $\vec{C}$ are vectors having unit magnitude. If $\vec{A} + \vec{B} + \vec{C} = \vec{0}$,then $\vec{A} \cdot \vec{B} + \vec{B} \cdot \vec{C} + \vec{C} \cdot \vec{A}$ will be:

Vectors $a \hat{i} + b \hat{j} + \hat{k}$ and $2 \hat{i} - 3 \hat{j} + 4 \hat{k}$ are perpendicular to each other. Given that $3a + 2b = 7$,and the ratio of $a$ to $b$ is $\frac{x}{2}$,find the value of $x$.

Two vectors $\vec{A} = 3\hat{i} + \hat{j}$ and $\vec{B} = \hat{j} + 2\hat{k}$ are given. Find the component of $\vec{A}$ along $\vec{B}$ in vector form.

If $\overrightarrow A = 3\hat i + \hat j + 2\hat k$ and $\overrightarrow B = 2\hat i - 2\hat j + 4\hat k$,then find $|\overrightarrow A \times \overrightarrow B |$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module