If a→=(1,1,0),b→=(1,1,1), then unit vector in the plane of a→ and b→ and perpendicular to a→ is

AP EAMCET · Maths · Vector Algebra

If $\vec{a} = (1, 1, 0), \vec{b} = (1, 1, 1)$ , then unit vector in the plane of $\vec{a}$ and $\vec{b}$ and perpendicular to $\vec{a}$ is

A $(0, 1, 0)$
B $(1, - 1, 0)$
C $\hat{k}$
D $(1, 0, 1)$

Verified Solution

Answer & Solution

Correct Answer

(C) $\hat{k}$

Step-by-step Solution

Detailed explanation

Let, u→ = xi^+yj^+zk^ is the required vector u→ = x2+y2+z2=1, since it is a unit vector Vectors in option 1 and 3 are the only units vectors Also, a→ is perpendicular to the vector so there dot product must be zero Only…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

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From AP EAMCET

Curve	Process
I	a) Adiabatic
II	b) Isobaric
III	c) Isochoric
IV	d) Isothermal

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