CBSE Class 12 Maths Vector Algebra Quiz 3

1. According to the associative lass of addition of addition of s ector

A \(\vec{b}\), \(\vec{a}\) B \(\vec{a}\), \(\vec{b}\) C \(\vec{a}\), 0 D \(\vec{b}\), 0

2. Which one of the following can be written for (\(\vec{a}\) – \(\vec{b}\)) × (\(\vec{a}\) + \(\vec{b}\))

A \(\vec{a}\) × \(\vec{b}\) B 2\(\vec{a}\) × \(\vec{b}\) C \(\vec{a}\)² – \(\vec{b}\) D 2\(\vec{b}\) × \(\vec{b}\)

3. The points with position vectors (2. 6), (1, 2) and (a, 10) are collinear if the of a is

A -8 B 4 C 3 D 12

4. |\(\vec{a}\) + \(\vec{b}\)| = |\(\vec{a}\) – \(\vec{b}\)| then the angle between \(\vec{a}\) and \(\vec{b}\)

A \(\frac{π}{2}\) B 0 C \(\frac{π}{4}\) D \(\frac{π}{6}\)

5. |\(\vec{a}\) × \(\vec{b}\)| = |\(\vec{a}\).\(\vec{b}\)| then the angle between \(\vec{a}\) and \(\vec{b}\)

A 0 B \(\frac{π}{2}\) C \(\frac{π}{4}\) D π

6. If ABCDEF is a regular hexagon then \(\vec{AB}\) + \(\vec{EB}\) + \(\vec{FC}\) equals

A zero B 2\(\vec{AB}\) C 4\(\vec{AB}\) D 3\(\vec{AB}\)

7. Which one of the following is the modulus of x\(\hat{i}\) + y\(\hat{j}\) + z\(\hat{k}\)?

A \(\sqrt{x^2+y^2+z^2}\) B \(\frac{1}{\sqrt{x^2+y^2+z^2}}\) C x² + y² + z² D none of these

8. If C is the mid point of AB and P is any point outside AB then,

A \(\vec{PA}\) + \(\vec{PB}\) = 2\(\vec{PC}\) B \(\vec{PA}\) + \(\vec{PB}\) = \(\vec{PC}\) C \(\vec{PA}\) + \(\vec{PB}\) = 2\(\vec{PC}\) = 0 D None of these

9. If \(\vec{OA}\) = 2\(\vec{i}\) – \(\vec{j}\) + \(\vec{k}\), \(\vec{OB}\) = \(\vec{i}\) – 3\(\vec{j}\) – 5\(\vec{k}\) then |\(\vec{OA}\) × \(\vec{OB}\)| =

A 8\(\vec{i}\) + 11\(\vec{j}\) – 5\(\vec{k}\) B \(\sqrt{210}\) C sin θ D \(\sqrt{40}\)

10. If |a| = |b| = |\(\vec{a}\) + \(\vec{b}\)| = 1 then |\(\vec{a}\) – \(\vec{b}\)| is equal to

A 1 B √3 C 0 D None of these