TS EAMCET 2023 (Online) 12th May Morning Shift | Vector Algebra Question 29 | Mathematics

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

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

$r=(t+1) \hat{\mathbf{i}}-(2 t-1) \hat{\mathbf{j}}+t \hat{\mathbf{k}}$

$\mathbf{r}=\hat{\mathbf{i}}+t \hat{\mathbf{j}}-t \hat{\mathbf{k}}$c

$\mathbf{r}=5 t \hat{\mathbf{i}}+7 t \hat{\mathbf{j}}+\hat{\mathbf{k}}$

TS EAMCET 2023 (Online) 12th May Morning Shift

MCQ (Single Correct Answer)

-0

The position vectors of the point $A, B$ are $\mathbf{a}, \mathbf{b}$ respectively. If the position vector of the point $C$ is $\frac{a}{2}+\frac{b}{3}$, then

$C$ lies inside $\triangle O A B$

C lies outside $\triangle O A B$ but inside $\angle A O B$

$C$ lies outside $\triangle O A B$ but inside $\angle O A B$

$C$ lies outside $\triangle O A B$ but inside $\angle O B A$

TS EAMCET 2023 (Online) 12th May Morning Shift

MCQ (Single Correct Answer)

-0

If $|\mathbf{a}|=1,|\mathbf{b}|=2,|\mathbf{a}-\mathbf{b}|^2+|\mathbf{a}+2 \mathbf{b}|^2=20$, then $(a, b)=$

$\frac{\pi}{3}$

$\frac{\pi}{4}$

$\frac{\pi}{6}$

$\frac{2 \pi}{3}$

TS EAMCET Subjects