Class 12 Vector Algebra worksheet

Sample questions

Real questions from this chapter, as the app sets them. Tap Answer to see the answer and working.

Section A · multiple choice

1. 1.

   The magnitude of 3î + 2ĵ − 6k̂ is:

   1. 7
   2. 49
   3. 11
   4. 8

   Answer

   (a) 7

   √(3² + 2² + (−6)²) = √49

2. 2.

   If a = −2î − 5ĵ + 4k̂ and b = −4î − 4ĵ − k̂, then a · b is:

   1. 32
   2. −12
   3. −24
   4. 24

   Answer

   (d) 24

   (−2)(−4) + (−5)(−4) + 4(−1)

3. 3.

   The unit vector in the direction of −12î − 12ĵ + k̂ is:

   1. (1/17)(12î + 12ĵ − k̂)
   2. (1/17)(−12î − 12ĵ + k̂)
   3. (1/289)(−12î − 12ĵ + k̂)
   4. (1/25)(−12î − 12ĵ + k̂)

   Answer

   (b) (1/17)(−12î − 12ĵ + k̂)

   divide by |a| = 17

Section B · short answer

1. 4.

   If a = 3î + ĵ + 5k̂ and b = −î + 3ĵ + 5k̂, find a + b, a − b and 4a − 4b.

   Answer

   a + b = 2î + 4ĵ + 10k̂; a − b = 4î − 2ĵ; 4a − 4b = 16î − 8ĵ

   add or subtract matching components

2. 5.

   Find the area of the parallelogram whose adjacent sides are 3î + 2ĵ + 2k̂ and −î.

   Answer

   2√2 square units

   a × b = −2ĵ + 2k̂; |a × b| = √8

Section C · long answer

1. 6.

   Show that the points A(3, −1, 5), B(6, 1, 4) and C(1, 0, 1) form a right-angled triangle, and find its area.

   Answer

   AB = 3î + 2ĵ − k̂, AC = −2î + ĵ − 4k̂; AB · AC = 0, so the right angle is at A; area = (7/2)√6 square units

   |AB × AC| = √294

Fresh sheets for your child

In the app, every Vector Algebra sheet is new: the app remembers the questions your child has already had and leaves them out. Print the sheet as a PDF, or use notebook mode and write the answers in a notebook.

Coming soon for Android and iPhone.

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