CBSE Class 12 Maths Vector Algebra Quiz 5

1. The vector having, initial and terminal points as (2, 5, 0) and (- 3, 7, 4) respectively is

A –\(\hat{i}\) + 12\(\hat{j}\) + 4\(\hat{k}\) B 5\(\hat{i}\) + 2\(\hat{j}\) – 4\(\hat{k}\) C -5\(\hat{i}\) + 2\(\hat{j}\) + 4\(\hat{k}\) D \(\hat{i}\) + \(\hat{j}\) + \(\hat{k}\)

2. Find the value of λ such that the vectors \(\vec{a}\) = 2\(\hat{i}\) + λ\(\hat{j}\) + \(\hat{k}\) and \(\vec{b}\) = \(\hat{i}\) + 2\(\hat{j}\) + 3\(\hat{k}\) are orthogonal

A 0 B 1 C \(\frac{3}{2}\) D –\(\frac{5}{2}\)

3. The value of λ for which the vectors 3\(\hat{i}\) – 6\(\hat{j}\) + \(\hat{k}\) and 2\(\hat{i}\) – 4\(\hat{j}\) + λ\(\hat{k}\) are parallel is

A \(\frac{2}{3}\) B \(\frac{3}{2}\) C \(\frac{5}{2}\) D –\(\frac{2}{5}\)

4. The vectors from origin to the points A and B are \(\vec{a}\) = 2\(\hat{i}\) – 3\(\hat{j}\) +2\(\hat{k}\) and \(\vec{b}\) = 2\(\hat{i}\) + 3\(\hat{j}\) + \(\hat{k}\) respectively, then the area of triangle OAB is

A 340 B \(\sqrt{25}\) C \(\sqrt{229}\) D \(\frac{1}{2}\) \(\sqrt{229}\)

5. For any vector \(\vec{a}\) the value of (\(\vec{a}\) × \(\vec{i}\))² + (\(\vec{a}\) × \(\hat{j}\))² + (\(\vec{a}\) × \(\hat{k}\))² is equal to

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

6. If |\(\vec{a}\)| = 10, |\(\vec{b}\)| = 2 and \(\vec{a}\).\(\vec{b}\) = 12, then the value of |\(\vec{a}\) × \(\vec{b}\)| is

A 5 B 10 C 14 D 16

7. The vectors λ\(\hat{i}\) + \(\hat{j}\) + 2\(\hat{k}\), \(\hat{i}\) + λ\(\hat{j}\) – \(\hat{k}\) and 2\(\hat{i}\) – \(\hat{j}\) + λ\(\hat{k}\) are coplanar if

A λ = -2 B λ = 0 C λ = 1 D λ = -1

8. If \(\vec{a}\), \(\vec{b}\), \(\vec{c}\) are unit vectors such that \(\vec{a}\) + \(\vec{b}\) + \(\vec{c}\) = \(\vec{0}\), then the value of \(\vec{a}\).\(\vec{b}\) + \(\vec{b}\).\(\vec{c}\) + \(\vec{c}\).\(\vec{a}\)

A 1 B 3 C –\(\frac{3}{2}\) D None of these

9. Projection vector of \(\vec{a}\) on \(\vec{b}\) is

A (\(\frac{\vec{a}.\vec{b}}{|\vec{b}|^2}\))\(\vec{b}\) B \(\frac{\vec{a}.\vec{b}}{|\vec{b}|}\) C \(\frac{\vec{a}.\vec{b}}{|\vec{a}|}\) D (\(\frac{\vec{a}.\vec{b}}{|\vec{a}|^2}\))\(\hat{b}\)

10. If \(\vec{a}\), \(\vec{b}\), \(\vec{c}\) are three vectors such that \(\vec{a}\) + \(\vec{b}\) + \(\vec{c}\) = 5 and |\(\vec{a}\)| = 2, |\(\vec{b}\)| = 3, |\(\vec{c}\)| = 5, then the value of \(\vec{a}\).\(\vec{b}\) +\(\vec{b}\).\(\vec{c}\) + \(\vec{c}\).\(\vec{a}\) is

A 0 B 1 C -19 D 38