The magnitude of the vector \(6 \hat{i}+2 \hat{j}+3 \hat{k}\) is

1

(a)

5

(b)

7

(c)

12

(d)

1

The angle between two vectors \(\vec{a} \text { and } \vec{b}\) with magnitude, \(\sqrt{3} \text { and } 4\) respectively and \(\vec{a} \cdot \vec{b}=2 \sqrt{3}\) is 

1

(a)

\(\frac{\pi}{6}\)

(b)

\(\frac{\pi}{3}\)

(c)

\(\frac{\pi}{2}\)

(d)

\(\frac{5 \pi}{2}\)

If \(\boldsymbol{\theta}\) is the angle between two vectors \(\vec{a} \text { and } \vec{b},\) then \(\vec{a} \cdot \vec{b} \geq 0\) only when

1

(a)

\(0<\theta<\frac{\pi}{2}\)

(b)

\(0 \leq \theta \leq \frac{\pi}{2}\)

(c)

\(0<\theta<\pi\)

(d)

\(0 \leq \theta \leq \pi\)

The value of \(\lambda\) for which the vectors \(\vec{a}=2 \hat{i}+\lambda \hat{j}+\hat{k} \text { and } \vec{b}=\hat{i}+2 \hat{j}+3 \hat{k}\) are orthogonal os

1

(a)

0

(b)

1

(c)

\(\frac{3}{2}\)

(d)

\(\frac{-5}{2}\)

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

1

(a)

5

(b)

10

(c)

14

(d)

16