Answer: Direction ratios of the x-axis are 1,0,0 and direction ratios of normal to the plane are 2,−3,−6. The angle between the line and the plane,...

### Find the vector equation of a line passing through the origin and perpendicular to the plane

Answer:

### Find the angle between the line and the plane 10x + 2y – 11z = 3.

Answer: Direction ratios of the given line are 2,3,6 Direction ratios of the normal to the given plane are 10,2,−11 The angle between the line and the plane: \begin{array}{l} \sin...

### Find the angle between the line and the plane

Answer: The equation of line is: $\vec{r}=(i+2 \hat{j}-\hat{k})+\lambda(\hat{i}-\hat{j}+\hat{k})$ Here, $\vec{b}=\hat{i}-j+\vec{k}$ The equation of plane is: r→·(2i^-j^+k^)=4 \vec{r}...

### Find the angle between the line and the plane

Answer: The equation of plane is: r→=(2i^-j^+3k^)+λ(3i^-j^+2k^) \vec{r}=(2 \hat{i}-\hat{j}+3 \hat{k})+\lambda(3 \hat{i}-\hat{j}+2 \hat{k}) On comparing with $\vec{r}=\vec{a}+\lambda...

### Find the value of m for which the line is parallel to the plane

Answer: Given equation of line, $\overrightarrow r = (\widehat i + 2\widehat k) + \lambda (2\widehat i - m\widehat j - 3\widehat k)$ Comparing with the line $\overrightarrow r = \overrightarrow...

### Find the angle between the line joining the points A(3,−4,−2) and B(12,2,0) and the plane 3x−y+z=1.

Answer:

### Show that the line line is parallel to the plane . Also, find the distance between them.

Answer: A line $\begin{array}{l} \overrightarrow r = \overrightarrow a + \lambda \overrightarrow b \\ \end{array}$ is parallel to the plane $\begin{array}{l} \overrightarrow r .\overrightarrow n ...

### Find the angle between the line and the plane

Answer: The equation of line is: r→=(3i^+k^)+λ(j^+k^) \vec{r}=(3 \hat{i}+\hat{k})+\lambda(\hat {j}+\hat{k}) Comparing with $\vec{r}=\vec{a}+\lambda \vec{b}$ $\vec{b}=(j+\dot{k})$. The...

### Find the angle between the line

and the plane

Answer: The given line is $\frac{x-2}{3}=\frac{y+1}{-1}=\frac{2-3}{2}$ ⇒r→=(2i→-j→+k→)+t(3i→-j→-2k→) \Rightarrow...

### Find the equation of the plane passing through each group of points: (i) A (2, 2, -1), B (3, 4, 2) and C (7, 0, 6) (ii) A (0, -1, -1), B (4, 5, 1) and C (3, 9, 4)

Answer: (i) Given, A (2, 2, -1) B (3, 4, 2) C (7, 0, 6) ...