Class 12th Mathematics Practice Set 1 | Vector Algebra | UP Board New Pattern Based

 

                                                                   PRACTICE SET - 1

                                      MODEL PAPER

                                      (Based On New Revised Syllabus)

                                                           Mathematics Class – 12

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Unit - Vector Algebra 

Q.1 Solve the following questions?                                           [ 2 mark each ]

            1.1 find the angle between vector ` i + j - k` and vector `i-j+k`

            1.2 find the angle between vector ` 2i + j +3k` and vector `3i-2j+k`

            1.3 find the angle between vector ` i + j +k` and vector `i-j-k`

            1.4 find the angle between vector ` 2i + j +3k` and vector `3i-2j+k`

            1.5 find the angle between vector ` i + j +9k` and vector `i-7j+k`

Q.2 Find the unit vectors of the following vecors?                                  [ 2 mark each ]

              2.1 Find the unit vector of vector ` i + j - k`

              2.2 Find the unit vector of vector ` i +5 j - k`

                 2.3 Find the unit vector of vector ` 2i + j +3k`

              2.4  Find the unit vector of vector `3i-2j+k`

              2.5 Find the unit vector of vector `i-7j+k`

Q.3 Find the projectile of vector `a` on vector `b`?                                [ 3 mark each ]

                3.1 Projectile of vector `7i+j-4k` on vector `2i+6j+3k`

                3.2 Projectile of vector `2i+3j+2k` on vector `i+2j+k`

                3.3 Projectile of vector `2i-j+k` on vector `i+j+k`

                3.4 Projectile of vector `i-2j+k` on vector `2i+j+k`

                3.5 Projectile of vector `2i+3j+2k` on vector `i+2j+k`

Q.4 Find the area of quadilateral whose diagonals are given as:          [ 5 mark each ]

                4.1 diagonal `d_1 = 3i+j+2k`  and  `d_2 = 2i-2j+4k`

                4.2 diagonal `d_1 = 3i+2j-k`  and  `d_2 = i-3j+2k`

Q.5 Find the area of a triangle whose to adjecent sides are represented by two vectors?

                                                                                                                                          [ 5 mark each ]  

                    5.1 Vector `a = 3i-j+5k`  and  `b = i+2j-k`

                  5.2 Vector `a = 3i+2j-k`  and  `b = i+3j-k`

Q.6 Find the area of a triangle whose position vectors of vertices are as follows?

                                                                                                                                            [ 5 mark each ]

                    6.1 `A (1, 1, 2),  B (2, -1, 1)  and C (3, 2, 1)`

                  6.2 `A (1, 1, 2),  B (2, 3, 5)  and C (1, 5, 5)`

Q.7 If vector `a = i+4j+2k`, vector `b = 3i-2j+7k`  and  vector  `c = 2i-j+4k` then find a vector `d` such that vector `d` is perpendicular to both vector `a &` vector `b` and vector `c.d = 15`

                                                                                                                             [ 8 mark each ]

Q.8 Find a vector `r` whose scalor product with vector `a,  b`  and  `c` are `-1, 6`  and  `5` respectively. Where 

Vector `a = 3i-5k`,  vector `b = 2i+7j` and vector `c = i+j+k`

                                                                                                                                [ 8 mark each ]

Q.9 From Vector method, prove that in a triangle ABC:

                        cos A = `\frac{\sqrt {b^2 + c^2 - a^2} }{2bc}`

                                                                                    [ 8 mark each ]

Q.10 From Vector method, prove that in a triangle ABC:

                `\frac{SinA}{a}` = `\frac{SinB}{b}` = `\frac{SinC}{c}`

Sine Formula                                                                                 [ 8 mark each ]   

                                                                                                    

                    

                                

                                                                            Practice Set 2