CBSE Guess > Papers > Important Questions > Class XII > 2011 > Maths > Maths By Mrs. E.Praveen
CBSE CLASS XII
Vectors-3D-Lines (4-Marks)
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- If A,B,C,D are four points in space prove that │AB x CD + BC x AD + CA x BD│ = 4 (Area ΔABC)
- If and , and find angle between
find the angle between
- For vectors and prove that :
- If with reference to a right handed system of mutually perpendicular unit vectors
, we have
and
Express
in the form
where
is perpendicular to
- Find the point on line
at a distance 3√2 from the point ( 1, 2, 3)
- Dot product of vector with vectors
are respectively -1,6 & 5 find the vector.
- Find image of the point (1,0,2) in the line passing through (2,1,3) and perpendicular to the lines
- Find the value of k so that the lines
and
are at right angle.
- . If
are any two non zero vectors.then prove that
- If
- If
Find a vector
which is perpendicular to
- Find the unit vector perpendicular to the plane ABC, where the position vectors of A, B & C are 2i – j + k, 3 i + j + 2 k & - 2 j + 3 k respectively.
- Dot product of a vector with the vector i + j - 3 k , i + 3 k - 2 k and 2 i + j + 4 k are 0, 5 and 8 respectively.find vector.
- find the shortest distance between the lines
=(1 - t ) i + (t - 2) j + ( 3 - 2 t ) k and r = ( s + 1 ) i +( 2 s - 1 ) j -( 2 s + 1) k
- find the equation of the line passing through the point(1,2,3) and parpendicular to lines
and
- The scalar product of the vector i + j + k with a unit vector along the sum of vectors 2i + 2j – 5k and λ i + 2j + 3k is equal to one. Find the value of λ .
- If a x b = c xd =, a x c = b xd, show that (a – d) is parallel to (b – c).
- Find the foot of perpendicular from P(1, 2, 3) on the line
Also find the equation of the plane containing the line and the point (1, 2, 3).
- Determine whether or not the following pair of lines intersect. If these intersect, then find the point of intersection, otherwise obtain the shortest distance between them: r = i + j – k + λ (3 i – j ) and r = 4 i – k + µ ( 2 i + 3 k )
- Find the foot of perpendicular from the point (0, 2, 7) on the line
Submitted By Mrs. E.Praveen
Email Id : [email protected]
