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Questions asked by balaji.thirumalai
Questions
4474
questions
1
answer selected
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
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
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
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
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
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
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
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
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
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
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
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
0
answers
If $$\overrightarrow{a} ,\overrightarrow{b} , \overrightarrow{c}$$ are mutually perpendicular vectors of equal magnitudes, show that the vector $$\overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c}$$ is equally inclined to $$\overrightarrow{a}, \overrightarrow{b} and \overrightarrow{c} $$.
cbse
class12
ch10
sec-b
math
asked
Nov 2, 2012
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
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
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
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
0
answers
Find a unit vector parallel to the vector....
cbse
class12
bookproblem
sec-a
easy
math
asked
Nov 2, 2012
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
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
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
0
answers
Determine the girl’s displacement from her initial point of departure.
cbse
class12
bookproblem
sec-a
easy
math
asked
Nov 2, 2012
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
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
1
answer
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