1 Marks Question

Question 11 Mark

Fill in the blanks :
(i) Plane formed by $x$-axis and $y$-axis is _________.
(ii) Coordinates of a point in XY-plane can be shown as _________.
(iii) Coordinate axes divide the space in __________ octants.

Answer

(i) $XY$ plane (ii) $(x, y, 0)$ (iii) $8$

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Question 21 Mark

Find the distance of point $P(\alpha, \beta, \gamma)$ from coordinate axes.

Answer

Distance from $x-axis$ $=\sqrt{\beta^2+\gamma^2}$,
Distance from $y-axis$ $=\sqrt{\alpha^2+\gamma^2}$,
Distance from $z-axis$ $=\sqrt{\alpha^2+\beta^2}$

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Question 31 Mark

Write the distances of point ( $x, y, z$ ) from three coordinate planes.

Answer

Let point $P \equiv(x, y, z)$
Distance of point P from $XY$ plane $=|z|$
Distance of point P from $YZ$ plane $=|x|$
Distance of point P from $ZX =|y|$

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Question 41 Mark

If distance between points $P (x,-8,4)$ and $Q(-3,-5,4)$ is 5 unit, then find the value of $x$.

Answer

Given points are $P \equiv(x,-8,4)$ and $Q \equiv(-3,-5,4)$
$\therefore \quad(PQ)^2=(x+3)^2+(-8+5)^2+(4-4)^2$
According to question, $PQ =5$ unit
$\begin{array}{l}\Rightarrow\quad(PQ)^2=25 \\\Rightarrow \quad(x+3)^2+(-3)^2+0=25 \\\Rightarrow \quad(x+3)^2=25-9=16 \\\Rightarrow \quad(x+3)= \pm 4 \\\Rightarrow \quad x=1,-7\end{array}$

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Question 51 Mark

In which octants are following points lie?
$(\text {i})$ $(3,-1,2)$$\quad$ $(\text {ii})$ $(3,1,2)$

Answer

(i) Since for point $A - x$ coordinate is poisitive, $y$ coordinate is negative and $z$ coordinate is positive. So point A is in octant $\text {OXY'Z}$.
(ii) Since for point $B -x, y$ and $z$ coordinates are positive. So point B lies in octant $\text {OXYZ}.$

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Question 61 Mark

Planes are drawn parallel to the coordinate planes through the points $(1,2,3)$ and $(3,-4,-5)$. Find the lengths of the edges of the parallelopiped so formed.

Answer

$\begin{array}{l}\left(\left|x_2-x_1\right|,\left|y_2-y_1\right|,\left|z_2-z_1\right|\right) \\=(|3-1|,|-4-2|,|-5-3|)=(2,6,8)\end{array}$

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