Vector 3D Questions

The shortest distance between line y - x = 1 and curve x = y2 is

The shortest distance between the line y - x = 1 and the curve x = y2 is

The shortest distance from the plane 12x + 4y + 3z = 327 to the sphere x2 + y2 + z2 + 4x - 2y - 6z = 155 is

Shortest distance between the lines and is -

A mirror and a source of light are situated at the origin O and at a point on OX respectively. A ray of light from the source along the x-axis strikes the mirror and is reflected. If the direction rat...

If the shortest distance between the lines (α ≠ − 1) and x + y + z + 1 = 0 = 2x − y +z + 3 is, then a value of α is :...

The shortest distance between the z-axis and the line x + y + 2z − 3 = 0 = 2x + 3y + 4z − 4, is :

Let $(\alpha,\beta,\gamma)$ be the co-ordinates of the foot of the perpendicular drawn from the point $(5,4,2)$ on the line $\overrightarrow{r} = ( - \widehat{i} + 3\widehat{j} + \widehat{k}) + \lambd...

Let the direction cosines of two lines satisfy the equations: $4\mathcal{l} + m - n = 0$ and $2mn + 10n\mathcal{l} + 3\mathcal{l}m = 0$.Then the cosine of the acute angle between these lines is :...

If the distances of the point $(1,2,a)$ from the line$\frac{x - 1}{1} = \frac{y}{2} = \frac{z - 1}{1}$ along the lines$L_{1}:\frac{x - 1}{3} = \frac{y - 2}{4} = \frac{z - a}{b}$ and$L_{2}:\frac{x - 1}...

Let $Q(a,b,c)$ be the image of the point $P(3,2,1)$ in the line $\frac{x - 1}{1} = \frac{y}{2} = \frac{z - 1}{1}$. Then the distance of Q from the line $\frac{x - 9}{3} = \frac{y - 9}{2} = \frac{z - 5...

The direction ratios of lines intersecting the line at angle 60o can be -