If vec{a} is a vector such that vec{a} times | vedclass

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

Question

(A) Let $\vec{a} = x \hat{i} + y \hat{j} + z \hat{k}$.Given $\vec{a} 	imes \hat{i} = \hat{j} + \hat{k}$.Calculating the cross product: $\vec{a} 	ime

Vedclass · Accepted Answer

$\vec{r}=(t+1) \hat{i}+(1-t) \hat{j}+(t+1) \hat{k}$

Vedclass · Answer

(A) Let $\vec{a} = x \hat{i} + y \hat{j} + z \hat{k}$.Given $\vec{a} 	imes \hat{i} = \hat{j} + \hat{k}$.Calculating the cross product: $\vec{a} 	imes \hat{i} = (x \hat{i} + y \hat{j} + z \hat{k}) 	imes \hat{i} = -y \hat{k} + z \hat{j} = z \hat{j} - y \hat{k}$.Comparing with $\hat{j} + \hat{k}$,we get $z = 1$ and $y = -1$.Given $\vec{a} \cdot \hat{i} = 1$,so $(x \hat{i} + y \hat{j} + z \hat{k}) \cdot \hat{i} = x = 1$.Thus,$\vec{a} = \hat{i} - \hat{j} + \hat{k}$.The equation of the line passing through point $\vec{p} = \hat{i} + \hat{j} + \hat{k}$ and parallel to $\vec{a}$ is $\vec{r} = \vec{p} + t \vec{a}$.$\vec{r} = (\hat{i} + \hat{j} + \hat{k}) + t(\hat{i} - \hat{j} + \hat{k}) = (1+t) \hat{i} + (1-t) \hat{j} + (1+t) \hat{k}$.

If $\vec{a}$ is a vector such that $\vec{a} \times \hat{i}=\hat{j}+\hat{k}$ and $\vec{a} \cdot \hat{i}=1$,then the equation of the line passing through the point $\hat{i}+\hat{j}+\hat{k}$ and parallel to $\vec{a}$ is

Similar Questions

If the two diagonals of a parallelogram are $\bar{d_1} = \bar{i} + 2\bar{j} + 3\bar{k}$ and $\bar{d_2} = -2\bar{i} + \bar{j} - 2\bar{k}$,then the area of the parallelogram in square units is

If $\overrightarrow{a}=2 \hat{i}-5 \hat{j}+8 \hat{k}$ and $\overrightarrow{b}=7 \hat{i}-5 \hat{j}+3 \hat{k}$ are two vectors and $(2 \overrightarrow{a}-3 \overrightarrow{b}) \times(4 \overrightarrow{a}+\overrightarrow{b})=x \hat{i}+y \hat{j}+z \hat{k}$,then $x+y+z=$

$(a - b) \times (a + b) = $

The area of the triangle,whose vertices are $A \equiv(1,-1,2)$,$B \equiv(2,1,-1)$ and $C \equiv(3,-1,2)$,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module