Let u→ be a vector coplanar with the vectors a→=2i^+3j^-k^ and b→= j^+k^ . If u→ is perpendicular to a→ and u→⋅b→=24, then u→^2 is equal to

Question

Let u→ be a vector coplanar with the vectors a→=2i^+3j^-k^ and b→= j^+k^ . If u→ is perpendicular to a→ and u→⋅b→=24, then u→^2 is equal to:

MARKS Content Team · Accepted Answer

Correct answer: (B) 336. As u → =λ[ a → ×( a → × b → ) ] u → =λ[ [ a → . b → ] a → −| a → |^2 b → ] u → =λ[ 2 a → −14 b → ] u → . b → =2λ[ a → . b → −7| b → |^2 ] =2λ[ 2−14 ] 24=−24λ λ=−1 u → =14 b → −2 a → u→=-4i^+8j^+16k^ | u → |^2 =4^2 +8^2 +16^2 =336

Let $\vec{u}$ be a vector coplanar with the vectors $\vec{a} = 2 \hat{i} + 3 \hat{j} - \hat{k}$ and $\vec{b} = \hat{j} + \hat{k}$ . If $\vec{u}$ is perpendicular to $\vec{a}$ and $\vec{u} \cdot \vec{b} = 24$ , then ${|\vec{u}|}^{2}$ is equal to:

Solution

Relevant Questions

Let u→ be a vector coplanar with the vectors a→=2i^+3j^-k^ and b→= j^+k^ . If u→ is perpendicular to a→ and u→⋅b→=24, then u→2 is equal to:

Solution

Relevant Questions

Let $\vec{u}$ be a vector coplanar with the vectors $\vec{a} = 2 \hat{i} + 3 \hat{j} - \hat{k}$ and $\vec{b} = \hat{j} + \hat{k}$ . If $\vec{u}$ is perpendicular to $\vec{a}$ and $\vec{u} \cdot \vec{b} = 24$ , then ${|\vec{u}|}^{2}$ is equal to: