A vector vec{r} of magnitude 3sqrt{2} units w | vedclass

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

Question

(A) Let the vector be $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$.The direction cosines are $l = \cos \alpha$, $m = \cos \beta$, $n = \cos \gamma$.Give

Vedclass · Accepted Answer

$\vec{r} = \pm 3\hat{i} + 3\hat{j}$

Vedclass · Answer

(A) Let the vector be $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$.The direction cosines are $l = \cos \alpha$, $m = \cos \beta$, $n = \cos \gamma$.Given $\beta = \pi/4$ and $\gamma = \pi/2$, so $m = \cos(\pi/4) = 1/\sqrt{2}$ and $n = \cos(\pi/2) = 0$.Since $l^2 + m^2 + n^2 = 1$, we have $l^2 + (1/\sqrt{2})^2 + 0^2 = 1$, which gives $l^2 + 1/2 = 1$, so $l^2 = 1/2$, hence $l = \pm 1/\sqrt{2}$.The vector is $\vec{r} = |\vec{r}|(l\hat{i} + m\hat{j} + n\hat{k}) = 3\sqrt{2}(\pm \frac{1}{\sqrt{2}}\hat{i} + \frac{1}{\sqrt{2}}\hat{j} + 0\hat{k}) = \pm 3\hat{i} + 3\hat{j}$.

$A$ vector $\vec{r}$ of magnitude $3\sqrt{2}$ units which makes angles of $\pi/4$ and $\pi/2$ respectively with $Y$ and $Z$ axes is:

Similar Questions

If the position vectors of the points $A, B, C$ are $i, j, k$ respectively and $P$ is a point such that $\overrightarrow{AB} = \overrightarrow{CP},$ then the position vector of $P$ is

If $|\vec{c}|^2 = 60$ and $\vec{c} \times (\hat{i} + 2\hat{j} + 5\hat{k}) = \vec{0}$,then a value of $\vec{c} \cdot (-7\hat{i} + 2\hat{j} + 3\hat{k})$ is

If $\overline{r} = -4 \hat{i} - 6 \hat{j} - 2 \hat{k}$ is a linear combination of the vectors $\overline{a} = -\hat{i} - 4 \hat{j} + 3 \hat{k}$ and $\overline{b} = -8 \hat{i} - \hat{j} + 3 \hat{k}$,then which of the following is true?

$A, B, C, D, E$ are five coplanar points,then $\overrightarrow{DA} + \overrightarrow{DB} + \overrightarrow{DC} + \overrightarrow{AE} + \overrightarrow{BE} + \overrightarrow{CE}$ is equal to

Let $A, B, C$ be distinct points with position vectors $\hat{i} + \hat{j}$,$\hat{i} - \hat{j}$,and $p\hat{i} - q\hat{j} + r\hat{k}$ respectively. If points $A, B, C$ are collinear,then which of the following can be correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module