MCQ
The straigth line $\frac{\text{x}-3}{3}=\frac{\text{y}-2}{1}=\frac{\text{z}-1}{0}$ is:
- Aparallel to x-axis
- Bparallel to y-axis
- Cparallel to z-axis
- ✓perpendicular to z-axis
✓
Answer
Correct option: D.
perpendicular to z-axis
We have
$\frac{\text{x}-3}{3}=\frac{\text{y}-2}{1}=\frac{\text{z}-1}{0}$
Also, the given line is parallel to the vector $\vec{\text{b}}=3\hat{\text{i}}+\hat{\text{j}}+0\hat{\text{k}}$
Let $\text{x}\hat{\text{i}}+\text{y}\hat{\text{j}}+\text{z}\hat{\text{k}}$ be parpendicular to the given line.
Now,
$3\text{x}+4\text{y}+0\text{z}=0$
It is satisfied by the coordinates of z-axis, i.e. (0, 0, 1).
Hence, the given line is perpendicular to z-axis.
$\frac{\text{x}-3}{3}=\frac{\text{y}-2}{1}=\frac{\text{z}-1}{0}$
Also, the given line is parallel to the vector $\vec{\text{b}}=3\hat{\text{i}}+\hat{\text{j}}+0\hat{\text{k}}$
Let $\text{x}\hat{\text{i}}+\text{y}\hat{\text{j}}+\text{z}\hat{\text{k}}$ be parpendicular to the given line.
Now,
$3\text{x}+4\text{y}+0\text{z}=0$
It is satisfied by the coordinates of z-axis, i.e. (0, 0, 1).
Hence, the given line is perpendicular to z-axis.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If the rate of chage of volume of sphere is equal to the rate of change of its radius, then its radius is equal to:
The value of the determinant $\left| {\,\begin{array}{*{20}{c}}1&a&{b + c}\\1&b&{c + a}\\1&c&{a + b}\end{array}\,} \right|$is
→$[a\,\,b\,\,a \times b]$ is equal to
→Let $f^{\prime}(x)=\frac{192 x^3}{2+\sin ^4 \pi x}$ for all $x \in R$ with $f\left(\frac{1}{2}\right)=0$. If $m \leq \int_{1 / 2}^1 f(x) d x \leq M$, then the possible values of $m$ and $M$ are
→The number of all $3 \times 3$ matrices $A$, with enteries from the set $\{-1,0,1\}$ such that the sum of the diagonal elements of $\mathrm{AA}^{\mathrm{T}}$ is $3,$ is
→The direction ratios of the normal to the plane $7x + 4y - 2z + 5 = 0$ are:
→Choose the correct answer from the given four options.
The feasible solution for a LPP is shown in. Let Z = 3x - 4y be the objective function.
Minimum of Z occurs at:
The feasible solution for a LPP is shown in. Let Z = 3x - 4y be the objective function.
Minimum of Z occurs at:
Let $f$ and $g$ are twice differentiable functions such that $f(x).g(x) = 1\,\, \forall x \in R$ and $f'$ and $g'$ are never zero, then $\frac{{f^{''}(x)}}{{f(x)}} + \frac{{g^{''}(x)}}{{g(x)}}$ equals-
→Assume that in a family, each chold is equally likely to be a boy or a girl. A family with tree cgildren is chosen at random. Tere probability that the eldest child is a girl given that the family has at least oe girl.
The area of the region bounded by $y=|| x-3|-4|-5$ and the $X$-axis is
→