Find the vector equation of the line passing through the point ha… - Vidyadip

Question

Find the vector equation of the line passing through the point having position vector $2 \hat{i}+\hat{j}-3 \hat{k}$ and perpendicular to vectors $\hat{i}+\hat{j}+\hat{k}$. and $\hat{i}+2 \hat{j}-\hat{k}$

✓

Answer

Let $a=2 \hat{i}+\hat{j}-3 \hat{k}, \bar{b}=\hat{i}+\hat{j}+\hat{k}$ and $\mathrm{c}=\hat{i}+2 \hat{j}-\hat{k}$
We know that $\bar{b} \times \bar{c}$ is perpendicular to both $\bar{b}$ and $\bar{c}$.
$\therefore \bar{b} \times \bar{c}$ is parallel to the required line.
$
\bar{b} \times \bar{c}=\left|\begin{array}{ccc}
\hat{i} & \hat{j} & \hat{k} \\
1 & 1 & 1 \\
1 & 2 & -1
\end{array}\right|=-3 \hat{i}+2 \hat{j}+\hat{k}
$
Thus required line passes through $a=2 \hat{i}+\hat{j}-3 \hat{k}$ and parallel to $-3 \hat{i}+2 \hat{j}+\hat{k}$.
$\therefore$ Its equation is $\bar{r}=(2 \hat{i}+\hat{j}-3 \hat{k})+\lambda(-3 \hat{i}+2 \hat{j}+\hat{k})$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(2 Marks)" from Line and Plane→Line and Plane — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Determine whether the following statement patterns are tautologies contradictions or contingencies : (p → q) ∧ (p ∧ ~q)

Find the probability distribution of : number of tails in the simultaneous tosses of three coins.

Show that $\text{f}(\text{x})=\text{x}+\cos\text{x}-\text{a}$ is an increasing function on R for all values of a.

If g (x) is a decreasing function on R and $\text{f}(\text{x})=\tan^{-1}[\text{g}(\text{x})].$ State whether f(x) is increasing or decreasing on R.

If $\text{A}=\begin{bmatrix}5&3&8\\2&0&1\\1&2&3\end{bmatrix}.$ Write the cofactor of element $a_{32}$.

Find gof and fog when $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by:
$f(x)=2 x+x^2$ and $g(x)=x^3$

Find the principal solutions of $\tan x=-\sqrt{3}$

Evaluate:
$\sin\Big(\tan^{-1}\text{x}+\tan^{-1}\frac{1}{\text{x}}\Big)\text{ for }\text{x}<0$

If A is a square matrix of order $3$ with determinant $4$, then write the value of $|-A|$.

Sketch the graph of inequation x ≥ 5y in xoy co-ordinate system