Let U→=i^+j^, V→=i^-j^ and W→=3i^+5j^+3k^. If n^ is a unit vector such that U→⋅n^=0 and V→⋅n^=0, then W→⋅n^ is equal to

Correct answer: 3. ∵ n^ is perpendicular to both U→ and V→ Hence, n^=λU→×V→ n^=±λ-2k^ Since n^ is unit vector hence n^=1 ⇒2λ=1 ⇒λ=1/2 Hence, n^=±k^ So, W→⋅n^=3

Q9 / 100 · NTA Abhyas (JEE Main) 2020 · Mathematics · Vector Algebra

Let $\vec{U} = \hat{i} + \hat{j}, \vec{V} = \hat{i} - \hat{j}$ and $\vec{W} = 3 \hat{i} + 5 \hat{j} + 3 \hat{k} .$ If $\hat{n}$ is a unit vector such that $\vec{U} \cdot \hat{n} = 0$ and $\vec{V} \cdot \hat{n} = 0$ , then $|\vec{W} \cdot \hat{n}|$ is equal to

Correct answer: 3

Solution

∵ \hat{n}

is perpendicular to both

\vec{U}

and

\vec{V}

Hence,

\hat{n} = λ (\vec{U} \times \vec{V})

\hat{n} = \pm λ (- 2 \hat{k})

Since

\hat{n}

is unit vector hence

|\hat{n}| = 1

\Rightarrow 2 λ = 1

\Rightarrow λ = \frac{1}{2}

Hence,

\hat{n} = \pm \hat{k}

So,

|\vec{W} \cdot \hat{n}| = 3

Hence, the correct answer is 3.

Let U→=i^+j^, V→=i^-j^ and W→=3i^+5j^+3k^. If n^ is a unit vector such that U→⋅n^=0 and V→⋅n^=0, then W→⋅n^ is equal to

Solution

More Vector Algebra Questions

Let $\vec{U} = \hat{i} + \hat{j}, \vec{V} = \hat{i} - \hat{j}$ and $\vec{W} = 3 \hat{i} + 5 \hat{j} + 3 \hat{k} .$ If $\hat{n}$ is a unit vector such that $\vec{U} \cdot \hat{n} = 0$ and $\vec{V} \cdot \hat{n} = 0$ , then $|\vec{W} \cdot \hat{n}|$ is equal to