If the vectors P→$$=ai^+aj^+3k^$$ and Q→$$=ai^$$−$$2j^$$−$$k^$$ are perpendicular to each then the value of a can be :

Correct option is 3both (1) and (2)

Questions

If the vectors $\vec{P} = a \hat{i} + a \hat{j} + 3 \hat{k}$ and $\vec{Q} = a \hat{i} - 2 \hat{j} - \hat{k}$ are perpendicular to each then the value of a can be :

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both (1) and (2)

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detailed solution

Correct option is C

P→.Q→=0 (If P→ and Q→ are perpendicular to each other) (ai^+aj^+3k^).(ai^−2j^−k^)=0 a.a−a.2−3.1=0 a2−2a−3=0 a2−3a+a−3=0 (a−3)(a+1)=0 a=3 and a=−1

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If the vectors P→=ai^+aj^+3k^ and Q→=ai^−2j^−k^ are perpendicular to each then the value of a can be :

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If the vectors $\vec{P} = a \hat{i} + a \hat{j} + 3 \hat{k}$ and $\vec{Q} = a \hat{i} - 2 \hat{j} - \hat{k}$ are perpendicular to each then the value of a can be :