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Recent questions tagged bookproblem
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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?
cbse
class12
bookproblem
ch12
misc
q1
p525
sec-c
medium
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
Choose the correct answer in the distance between the two planes: $2x + 3y + 4z = 4$ and $4x + 6y + 8z = 12$ is
cbse
class12
bookproblem
ch11
misc
p499
q22
sec-b
medium
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
Prove that if a plane has the intercepts a, b, c and is at a distance of p units from the origin, then $$1/a^2 + 1/b^2 + 1/c^2 = 1/p^2$$
cbse
class12
bookproblem
sec-c
difficult
math
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 $\frac{\large x-15}{\large 3} = \frac{\large y-29}{\large 8} = \frac{\large z-5}{\large -5}$
cbse
class12
bookproblem
ch11
misc
p499
q20
sec-c
medium
math
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 $\hat{r} (3\hat{i} + \hat{j} + \hat{k} ) = 6$
cbse
class12
bookproblem
ch11
misc
p499
q19
sec-c
difficult
math
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 $\hat{r} . (\hat{ i} -\hat{ j} + \hat{k} ) = 5$
cbse
class12
bookproblem
ch11
misc
p499
q18
sec-c
medium
math
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.
cbse
class12
bookproblem
ch11
misc
p499
q16
sec-b
medium
math
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 $\hat{r} . (5\hat{i} + 3\hat{j} -6\hat{k}) +8 = 0$
cbse
class12
bookproblem
ch11
misc
p499
q17
sec-b
medium
math
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 $p$.
cbse
class12
bookproblem
ch11
misc
p498
q14
sec-c
difficult
math
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 $3x + 3y + z = 0$.
cbse
class12
bookproblem
ch11
misc
p498
q13
sec-c
medium
math
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 $2x + y + z = 7.$
cbse
class12
bookproblem
ch11
misc
p498
q12
sec-b
medium
math
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.
cbse
class12
bookproblem
ch11
misc
p498
q10
sec-b
medium
math
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 ZX-plane.
cbse
class12
bookproblem
ch11
misc
p498
q11
sec-b
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
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 $\hat{r} = - 4\hat{i} - \hat{k} + \mu (3\hat{i} - 2\hat{j} - 2\hat{k} )$
cbse
class12
bookproblem
ch11
misc
p498
q9
sec-b
easy
math
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 $\hat{r} . (\hat{i} +2\hat{j} -5\hat{k}) +9 = 0$
cbse
class12
bookproblem
ch11
misc
p498
q7
sec-a
easy
math
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 $k$.
cbse
class12
bookproblem
ch11
misc
p498
q6
sec-a
easy
math
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 $CD$.
cbse
class12
bookproblem
ch11
misc
p498
q5
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
Find the equation of a line parallel to x-axis and passing through the origin.
cbse
class12
bookproblem
ch11
misc
p498
q4
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
Find the angle between the lines whose direction ratios are $a, b, c$ and $b -c, c -a, a - b.$
cbse
class12
bookproblem
ch11
misc
p498
q3
sec-a
easy
math
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 $m_1n_2-m_2n_1$, $n_1l_2-n_2l_1$, $l_1m_2-l_2m_1$
cbse
class12
bookproblem
ch11
misc
p497
q2
difficult
sec-b
math
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).
cbse
class12
bookproblem
ch11
misc
p497
q1
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
What is the value of $$\hat{i} (\hat{j}. \hat{k}) \hat{j} (\hat{i}. \hat{k}) \hat{k} (\hat{j}. \hat{i})?$$
cbse
class12
bookproblem
sec-a
medium
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
If $\theta$ is the angle between any two vectors $ \overrightarrow{a} and \overrightarrow{b} ,$ then $|\overrightarrow{a}.\overrightarrow{b} | = | \overrightarrow{a} \times \overrightarrow{b} | $ when $\theta$ is equal to
bookproblem
class12
cbse
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
If θ is the angle between two vectors $$\overrightarrow{a} and \overrightarrow{b}$$ when is $$\overrightarrow{a} ⋅ \overrightarrow{b} ≥ 0$$
cbse
class12
bookproblem
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
Prove that $$(\overrightarrow{a} + \overrightarrow{b} ) ⋅ (\overrightarrow{a} + \overrightarrow{b} ) =| \overrightarrow{a} |2 + | \overrightarrow{b} |2$$ if and only if $$\overrightarrow{a} , \overrightarrow{b}$$ are perpendicular, given $$\overrightarrow{a} ≠ 0, \overrightarrow{b} ≠ 0$$
cbse
class12
bookproblem
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
0
answers
Given $$\overrightarrow{a}, \overrightarrow{b} and \overrightarrow{c}$$ Find a vector $$\overrightarrow{d}$$ which is perpendicular to both $$\overrightarrow{a} and \overrightarrow{b}, and \overrightarrow{c} ⋅\overrightarrow{d} = 15$$
bookproblem
cbse
class12
sec-a
easy
ch10
math
asked
Nov 2, 2012
by
anonymous
0
answers
Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are $1 / \sqrt{3}, 1 / \sqrt{3}$ and $1 / \sqrt{3} $
cbse
class12
bookproblem
sec-a
math
asked
Nov 2, 2012
by
balaji.thirumalai
0
answers
The two adjacent sides of a parallelogram are given. Find the unit vector parallel to its diagonal. Also, find its area.
cbse
class12
bookproblem
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
0
answers
Find the position vector of a point tand show that P is the mod point of the line segment
cbse
class12
bookproblem
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
0
answers
Show that the points A (1, – 2, – 8), B (5, 0, – 2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.
cbse
class12
bookproblem
sec-b
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
0
answers
Find a unit vector parallel to the vector....
cbse
class12
bookproblem
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
0
answers
Find a vector of magnitude 5 units, and parallel to the resultant of the vectors
cbse
class12
bookproblem
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
0
answers
Find the value of x for which $$ x(\hat{i} + \hat{j}+ \hat{k})$$ is a unit vector
cbse
class12
bookproblem
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
0
answers
If$$ \overrightarrow {a} = \overrightarrow {b} + \overrightarrow {c} $$ If this is the case, then is it true that $$ |\overrightarrow {a}| = |\overrightarrow {b}| + |\overrightarrow {c}| $$
cbse
class12
bookproblem
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
0
answers
Determine the girl’s displacement from her initial point of departure.
cbse
class12
bookproblem
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
0
answers
Find the scalar components and magnitude of the vector joining the points $P (x_1, y_1, z_1)$ and $Q (x_2, y_2, z_2)$.
cbse
class12
bookproblem
sec-a
easy
ch10
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of x-axis.
cbse
class12
bookproblem
ch10
concepts
toolbox
sec-a
easy
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
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