Fill In The Blanks[1 Marks ]

Question 11 Mark

If the coordinates of the points $A , B , C$ and D are respectively $(1,2,3),(4,5,7),(-4,3,-6)$ and $(2,9,2)$, then the angle between the lines AB and CD will be an acute angle ____________ .

Answer

$\quad 0^{\circ}$ (Zero degree $)$

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Question 21 Mark

The equations of a line passing through origin and parallel to $x$-axis are _________ .

Answer

$\frac{x}{1}=\frac{y}{0}=\frac{z}{0}$

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Question 31 Mark

A line passing through origin and parallel to z-axis is _________ .

Answer

$\frac{x}{0}=\frac{y}{0}=\frac{z}{1}$

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Question 41 Mark

The condition of parallelism of two lines is __________ .

Answer

$\frac{l_1}{l_2}=\frac{m_1}{m_2}=\frac{n_1}{n_2}$ or $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

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Question 51 Mark

If the direction cosines of a line are $l, m, n$, then the equations of the line are _____________ .

Answer

$\frac{x-x_1}{l}=\frac{y-y_1}{m}=\frac{z-z_1}{n}$

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Question 61 Mark

If a line makes equal angles with the coordinate axes, then its direction cosines will be ___________ .

Answer

$\pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}$

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Question 71 Mark

The direction cosines of $x$-axis are ___________ .

Answer

$1,0,0$

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Question 81 Mark

The direction cosines of a line parallel to any co-ordinate axis are equal to the _________ of the corresponding coordinate axis.

Answer

Direction-cosines

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Question 91 Mark

To obtain the direction cosines from the direction ratios $a, b, c$ of the line, we divide $a, b, c$ by ___________ .

Answer

$\sqrt{a^2+b^2+c^2}$

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Question 101 Mark

If any vector makes angle $\pi-\alpha, \pi-\beta$ and $\pi-\gamma$ with axes $OX , OY$ and OZ , then the direction cosines of $\overrightarrow{ PO }$ will be ____________ .

Answer

$-\cos \alpha,-\cos \beta,-\cos \gamma$ or $-l,-m,-n$

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MATHS Fill In The Blanks[1 Marks ]

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