Let a = i + 2j + 3k and b = -2i + 3j - 4k, then which of the following statements are correct? (A) |a| = sqrt(14) (B) |b| = 29 (C) a * b = 8 (D) Angle between a and b is ^-1(-8sqrt(406)) Choose the correct answer from the options given below: Option 1: (A) and (D) only Option 2: (A) and (C) only Option 3: (B), (C) and (D) only Option 4: (A), (C) and (D) only

The answer is '(A) and (D) only'. View full solution:

Algebra > Vector Algebra

Medium

core

Let $\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k}$ and $\vec{b} = -2\hat{i} + 3\hat{j} - 4\hat{k}$, then which of the following statements are correct? (A) $|\vec{a}| = \sqrt{14}$ (B) $|\vec{b}| = 29$ (C) $\vec{a} \cdot \vec{b} = 8$ (D) Angle between $\vec{a}$ and $\vec{b}$ is $\cos^{-1}\left(\frac{-8}{\sqrt{406}}\right)$ Choose the correct answer from the options given below:

(A) and (D) only

(A) and (C) only

(B), (C) and (D) only

(A), (C) and (D) only

✅ Correct Option: 1

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