Recent questions tagged misc

Refer to Example 9 in book ( page 521 - copied below ). (Diet problem) A dietician has to develop a special diet using two foods P and Q. Each packet (containing 30 g) of food P contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin A. Each packet of the same quantity of food Q contains 3 units of calcium, 20 units of iron, 4 units of cholesterol and 3 units of vitamin A. The diet requires atleast 240 units of calcium, atleast 460 units of iron and at most 300 units of cholesterol. How many packets of each food should be used to minimise the amount of vitamin A in the diet? What is the minimum amount of vitamin A?How many packets of each food should be used to maximise the amount of vitamin A in the diet? What is the maximum amount of vitamin A in the diet?

asked Nov 2, 2012 by balaji.thirumalai

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Choose the correct answer in the distance between the two planes: $2x + 3y + 4z = 4$ and $4x + 6y + 8z = 12$ is

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Find the vector equation of the line passing through (1, 2, -4) and perpendicular to the two lines $\frac{\large x-8}{\large 3} = \frac{\large y+19}{\large -16} = \frac{\large z-10}{\large 7}$ and $\frac{\large x-15}{\large 3} = \frac{\large y-29}{\large 8} = \frac{\large z-5}{\large -5}$

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Find the vector equation of the line passing through $(1, 2, 3)$ and parallel to the planes $\hat{r}. (\hat{i} - \hat{j} + 2\hat{k}) = 5$ and $\hat{r} (3\hat{i} + \hat{j} + \hat{k} ) = 6$

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Find the distance of the point (-1, -5, -10) from the point of intersection of the line $\hat{r} = 2\hat{i} - \hat{j} + 2\hat{k} + \lambda (3\hat{i} + 4\hat{j} + 2\hat{k}) $ and the plane $\hat{r} . (\hat{ i} -\hat{ j} + \hat{k} ) = 5$

asked Nov 2, 2012 by balaji.thirumalai

1 answer

If O be the origin and the coordinates of P be $(1, 2, – 3)$, then find the equation of the plane passing through P and perpendicular to OP.

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Find the equation of the plane which contains the line of intersection of the planes $\hat{r} . (\hat{i} + 2\hat{j} +3\hat{k}) - 4 = 0$ and $\hat{r} . (2\hat{i} + \hat{j} - \hat{k}) + 5 = 0$ and which is perpendicular to the plane $\hat{r} . (5\hat{i} + 3\hat{j} -6\hat{k}) +8 = 0$

asked Nov 2, 2012 by balaji.thirumalai

1 answer

If the points $( 1, 1 , p)$ and $(– 3 , 0, 1)$ be equidistant from the plane $\hat{r} . (3\hat{i} +4\hat{j} -12\hat{k} +13) = 0$ then find the value of $p$.

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Find the equation of the plane passing through the point $( -1, 3, 2)$ and perpendicular to each of the planes $x + 2y + 3z = 5$ and $3x + 3y + z = 0$.

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Find the coordinates of the point where the line through $(3, – 4, – 5)$ and $(2, – 3, 1)$ crosses the plane $2x + y + z = 7.$

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Find the coordinates of the point where the line through $(5, 1, 6)$ and $(3, 4, 1)$ crosses the YZ-plane.

asked Nov 2, 2012 by balaji.thirumalai

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Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the ZX-plane.

asked Nov 2, 2012 by balaji.thirumalai

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Find the shortest distance between lines $\hat{r} = 6\hat{i} + 2\hat{j} + 2\hat{k} + \lambda ( \hat{i} - 2\hat{j} + 2\hat{k} )$ and $\hat{r} = - 4\hat{i} - \hat{k} + \mu (3\hat{i} - 2\hat{j} - 2\hat{k} )$

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Find the vector equation of the line passing through $(1, 2, 3)$ and perpendicular to the plane $\hat{r} . (\hat{i} +2\hat{j} -5\hat{k}) +9 = 0$

asked Nov 2, 2012 by balaji.thirumalai

1 answer

If the lines $\large\frac{x-1} {-3} = \frac{y-2}{2k} = \frac{z-3}{2}$ and $\large\frac{x-1}{3k} = \frac{y-1}{1} = \frac{z-6}{-5}$ are perpendicular, find the value of $k$.

asked Nov 2, 2012 by balaji.thirumalai

1 answer

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

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Find the equation of a line parallel to x-axis and passing through the origin.

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Find the angle between the lines whose direction ratios are $a, b, c$ and $b -c, c -a, a - b.$

asked Nov 2, 2012 by balaji.thirumalai

1 answer

If $ l_1, m_1, n_1$ and $l _2, m_2, n_2 $ are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are $m_1n_2-m_2n_1$, $n_1l_2-n_2l_1$, $l_1m_2-l_2m_1$

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, – 1), (4, 3, – 1).

asked Nov 2, 2012 by balaji.thirumalai

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