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
.
- Show that the points A, B, C with position vectors
respectively are collinear
- If the sum of two unit vectors is a unit vector, Prove that the magnitude of their difference is
.
- Show that the points A, B and C with position vectors,
respectively, form the vertices of a right angled triangle.
- If a unit vector
makes angles
and
then find θ and hence the components of
.
- Let
, and be three vectors such that and each one of them being perpendicular to the sum of other two, Find
- Find the area of the parallelogram whose adjacent sides are determined by the vectors
- The scalar product of the vector
with a unit vector along the sum of vectors
Find the value of λ.
- If
is any vector in space show tha
- If vectors
, and are such | a + b + c | =0, and | a | = 6, | b | = 8 and | c | = 10. Find (a.b+b.c+c.a)
- Find the vector of magnitude 5 units which is perpendicular to both the vectors
- Find the values of
.
- Show that area of parallelogram having diagonals (3i + j – 2k) and (i – 3j + 4k) is 5 √3 sq unit.
- Find the shortest distance between the lines, whose equations are
- Find shortest distance between the lines r = i + j +λ (2i – j + k), r = 2i + j – k + μ (3i – 5j + 2k)
- If
then find the value of
.
- By computing the shortest distance, determine whether the following pair of lines intersect or not:
- d1 and d2 are the diagonals of a parallelogram with sides a and b.Express a and b in terms of d1 and d2 and find the area of the parallelogram ;d1 = i + 2 j + 3 k ;d2 = 3 i - 2 j + k
- Find the shortest distance between the following pairs of line r = (1 – t ) i + ( t – 2 ) j + ( 3 + 2t ) k and r = ( s + 1) i + ( 2s – 1) j + ( 2s + 1 ) k.
- Find the equations of the line through the intersection of the lines
and
and parallel to the line
Submitted By Mrs. E.Praveen
Email Id : [email protected]
