List of top Mathematics Questions

The scalar product of the vector \(\hat i+\hat j+\hat k \) with a unit vector along the sum of vectors \(2\hat i+4\hat j-5 \hat k\) and \(\lambda \hat i+2\hat j+3\hat k\) is equal to one. Find the value of λ.

Find the vector and the cartesian equations of the line that passes through the points(3,-2,-5),(3,-2,6).
In triangle ABC which of the following is not true.
Vector
Show that the points \(A, B,\) and \(C\) with position vectors, \(\vec{a}=3\hat{i}-4\hat{j}-4\hat{k}, \vec{b}=2\hat{i}-\hat{j}+\hat{k}\) and \(\vec{c}=\hat{i}-3\hat{j}-5\hat{k}\), respectively from the vertices of a right angled triangle.

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

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

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

It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles 9 are defective?

Find the area of the region bounded by the ellipse \(\frac{x2}{4}+\frac{y^2}{9}=1\)
Find the position vector of the mid point of the vector joining the points \(P(2,3,4)\) and \(Q(4,1,-2)\).
Find a position vector of a point \(R\) which devides the line joining two points \(P\) and \(Q\) whose position vectors are \(\hat{i}+2\hat{j}-\hat{k}\) and 
\(\hat{i}+\hat{j}+\hat{k}\) respectively,in the ratio \(2\ratio 1\)
(i)internally
(ii)externally

Find the shortest distance between lines \(\overrightarrow{r}\)=\(6\hat i+2\hat j+2\hat k\)+λ(\(\hat i+2\hat j+2\hat k\))and\(\overrightarrow{r}\)=-\(-4\hat i-\hat k\)+μ(\(3\hat i+2\hat j+2\hat k\)).

Find the probability of throwing at most 2 sixes in 6 throws of a single die.
Show that the vector \(\hat{i}+\hat{j}+\hat{k}\) is equally inclined to the axes OX,OY,and OZ.

If the vertices \(A,B,C\) of a triangle \(ABC\) are\((1,2,3),(-1,0,0),(0,1,2)\), respectively,then find \(\angle{ABC}\).[\(\angle{ABC}\) is the triangle between the vectors\( \overrightarrow{BA}\)and \( \overrightarrow{BC}\)].

Find the direction cosines of the vector joining the points \(A(1,2,-3)\) and \(B(-1,-2,1)\) directed from \(A\) to \(B\).

Find the equation of the plane passing through (a,b,c)and parallel to the plane \(\overrightarrow{r}\).(\(\hat i+\hat j+\hat k\))=2.

Find the direction cosines of the vector \(\hat{i}+2\hat{j}+3\hat{k}.\)
Find the probability of getting 5 exactly twice in 7 throws of die.

Find the vector equation of the plane passing through (1,2,3)and perpendicular to the plane r→.(i^+2j^-5k^)+9=0.

Show that the vectors \(2\hat{i}-3\hat{j}+4\hat{k}\) and \(-4\hat{i}+6\hat{k}-8\hat{k}\) are collinear.
Find a vector in a direction of vector \(5\hat{i}-\hat{j}+2\hat{k}\) which has magnitude 8units.

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

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.

A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a price is \(\frac{1}{100}\). What is the probability that he will win a prize:
(a) at least once
(b) exactly once
(c) at least twice?