If a → = i ^ + 2 j ^ + 3 k ^ , b → = - i ^ + 2 j ^ + k ^ , c → = 3 i ^ + j ^ and a → + p b → is normal to c → , then p is equal to

a → + p b → is normal to c → ∴ a → + p b → · c → = 0 1 - p i ^ + 2 + 2 p j ^ + 3 + p k ^ · 3 i ^ + j ^ = 0 3 - 3 p + 2 + 2 p = 0 ⇒ p = 5

Mathematics - Vector Question with Solution | TestHub

MathematicsVectorDot Product & Its Application ( Projection etc.)Easy2 minPYQ_2019

MathematicsEasysingle choice

If $\vec{a} = \hat{i} + 2 \hat{j} + 3 \hat{k}, \vec{b} = - \hat{i} + 2 \hat{j} + \hat{k}, \vec{c} = 3 \hat{i} + \hat{j}$ and $\vec{a} + p \vec{b}$ is normal to $\vec{c}$ , then $p$ is equal to

Options:

Answer:

Solution:

$(\vec{a} + p \vec{b})$ is normal to $\vec{c}$

$∴ (\vec{a} + p \vec{b}) \cdot \vec{c} = 0$

$((1 - p) \hat{i} + (2 + 2 p) \hat{j} + (3 + p) \hat{k}) \cdot (3 \hat{i} + \hat{j}) = 0$

$3 - 3 p + 2 + 2 p = 0 \Rightarrow p = 5$

Stream:BITSATSubject:MathematicsTopic:VectorSubtopic:Dot Product & Its Application ( Projection etc.)

⏱ 2mℹ️ Source: PYQ_2019

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