Question

$\vec { A } = 2 \hat { i } + 4 \hat { j } + 4 \hat { k }$ and $\vec { B } = 4 \hat { i } + 2 \hat { j } - 4 \hat { k }$ are two vectors. The angle between them will be

• A. 0⁰
• B. 45⁰
• C. 60⁰
• D. 90⁰

Answer 1

Answer: (D)

90⁰

Answer 2

$\cos \theta = \frac { \overrightarrow { \mathrm { A } } \cdot \vec { B } } { | \overrightarrow { \mathrm { A } } | \cdot | \vec { B } | } = \frac { a _ { 1 } b _ { 1 } + a _ { 2 } b _ { 2 } + a _ { 3 } b _ { 3 } } { | \overrightarrow { \mathrm { A } } | \cdot | \vec { B } | }$

$= \frac { 2 \times 4 + 4 \times 2 - 4 \times 4 } { | \vec { A } | \cdot | \vec { B } | } = 0$

∴ $\theta = \cos ^ { - 1 } \left( 0 ^ { \circ } \right)$ $\Rightarrow \theta = 90 ^ { \circ }$