Find Plus2 Important Maths 5 Mark Questions Part 4 in this post. For more practice questions on Maths, refer to the other parts in the 'Related Post' section.
1) If
and 
verify that
(i)^{-1}=B^{-1}A^{-1} )
(ii)^T=B^TA^T )
2) Solve: x + y+ 2x = 0; 3x + 2y +z = 0; 2x + y –z =0
3) Solve the following homogenous linear equations: x + 2y – 5z = 0; 3x + 4y + 6z = 0; x + y + z = 0
4) (i) For any vector
, prove that \overrightarrow{i}+(\overrightarrow{r}.\overrightarrow{j})\overrightarrow{j}+(\overrightarrow{r}.\overrightarrow{k})\overrightarrow{k} )
(ii) Find the projection of the vector
on 
5) Angle in a semi-circle is a right angle. Prove by vector method.
6) Find the vectors of magnitude 6 which are perpendicular to both the vector
and 
7) Show that the torque above the point A(3, –1, 3) of a force
through the point B(5, 2, 4) is 
8) If = \frac{\pi}{6} )
and  = 2\frac{\pi}{3} )
, then prove |z|=1.
9) If
, prove that
(i) )
(ii) )
10) Find all the values:^{\frac{2}{3}} )
11) Prove that if
, then 
12) A reflecting telescope has a parabolic mirror for which the distance from the vertex to the focus is 9 mts. If the distance across (diameter) the top of the mirror is 160 cm, how deep is the mirror at the middle?
13) Find the equation of the ellipse whose vertices are (-1, 4) and (-7, 4) and eccentricity is
14) Find the equations of the tangent and normal to the hyperbola
at 
15) Find the angle between the asymptotes of the hyperbola
OR
Show that the tangent to a rectangular hyperbola terminated by its asymptotes is bisected at the point of contact.
1) If
(i)
(ii)
2) Solve: x + y+ 2x = 0; 3x + 2y +z = 0; 2x + y –z =0
3) Solve the following homogenous linear equations: x + 2y – 5z = 0; 3x + 4y + 6z = 0; x + y + z = 0
4) (i) For any vector
(ii) Find the projection of the vector
5) Angle in a semi-circle is a right angle. Prove by vector method.
6) Find the vectors of magnitude 6 which are perpendicular to both the vector
7) Show that the torque above the point A(3, –1, 3) of a force
8) If
9) If
(i)
(ii)
10) Find all the values:
11) Prove that if
12) A reflecting telescope has a parabolic mirror for which the distance from the vertex to the focus is 9 mts. If the distance across (diameter) the top of the mirror is 160 cm, how deep is the mirror at the middle?
13) Find the equation of the ellipse whose vertices are (-1, 4) and (-7, 4) and eccentricity is
14) Find the equations of the tangent and normal to the hyperbola
15) Find the angle between the asymptotes of the hyperbola
OR
Show that the tangent to a rectangular hyperbola terminated by its asymptotes is bisected at the point of contact.
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