Science (English Medium) कक्षा ११ - CBSE Question Bank Solutions

Determine the point on z-axis which is equidistant from the points (1, 5, 7) and (5, 1, –4).

Find the point on y-axis which is equidistant from the points (3, 1, 2) and (5, 5, 2).

Find the points on z-axis which are at a distance \[\sqrt{21}\]from the point (1, 2, 3). 

Prove that the triangle formed by joining the three points whose coordinates are (1, 2, 3), (2, 3, 1) and (3, 1, 2) is an equilateral triangle.

Show that the points A(3, 3, 3), B(0, 6, 3), C(1, 7, 7) and D(4, 4, 7) are the vertices of a square.

Prove that the point A(1, 3, 0), B(–5, 5, 2), C(–9, –1, 2) and D(–3, –3, 0) taken in order are the vertices of a parallelogram. Also, show that ABCD is not a rectangle.

Find the coordinates of the point which is equidistant  from the four points O(0, 0, 0), A(2, 0, 0), B(0, 3, 0) and C(0, 0, 8).

If A(–2, 2, 3) and B(13, –3, 13) are two points.
Find the locus of a point P which moves in such a way the 3PA = 2PB.

Find the locus of P if PA² + PB² = 2k², where A and B are the points (3, 4, 5) and (–1, 3, –7).

Show that the points (a, b, c), (b, c, a) and (c, a, b) are the vertices of an equilateral triangle. 

Are the points A(3, 6, 9), B(10, 20, 30) and C(25, –41, 5), the vertices of a right-angled triangle?

Verify the following: 

 (0, 7, –10), (1, 6, –6) and (4, 9, –6) are vertices of an isosceles triangle.

Verify the following: 

 (0, 7, –10), (1, 6, –6) and (4, 9, –6) are vertices of an isosceles triangle. 

Verify the following: 

(0, 7, 10), (–1, 6, 6) and (–4, 9, –6) are vertices of a right-angled triangle.

Verify the following: 

 (–1, 2, 1), (1, –2, 5), (4, –7, 8) and (2, –3, 4) are vertices of a parallelogram.

Verify the following:

 (5, –1, 1), (7, –4,7), (1, –6,10) and (–1, – 3,4) are the vertices of a rhombus.

Find the locus of the points which are equidistant from the points (1, 2, 3) and (3, 2, –1).

Find the locus of the point, the sum of whose distances from the points A(4, 0, 0) and B(–4, 0, 0) is equal to 10.

Show that the points A(1, 2, 3), B(–1, –2, –1), C(2, 3, 2) and D(4, 7, 6) are the vertices of a parallelogram ABCD, but not a rectangle.

Write the sum of the coefficients in the expansion of \[\left( 1 - 3x + x^2 \right)^{111}\]