Vectors a→, b→, c→, d→ are such that (a→×b→)×(c→×d→)=0→. P1 and P2 are two planes determined by vectors a¯, b¯ and c¯, d¯, respectively. Then the angle between the planes P1 and P2 is

TS EAMCET · Maths · Three Dimensional Geometry

Vectors $\vec{a}, \vec{b}, \vec{c}, \vec{d}$ are such that $(\vec{a} \times \vec{b}) \times (\vec{c} \times \vec{d}) = \vec{0} . P_{1}$ and $P_{2}$ are two planes determined by vectors $\bar{a}, \bar{b}$ and $\bar{c}, \bar{d}$ , respectively. Then the angle between the planes $P_{1}$ and $P_{2}$ is

A $0$
B $\frac{π}{4}$
C $\frac{π}{3}$
D $\frac{π}{2}$

Verified Solution

Answer & Solution

Correct Answer

(A) $0$

Step-by-step Solution

Detailed explanation

Let, N1→ and N2→ are the normals of planes P1 and P2, respectively. ∴a→×b→=N1→ & c→×d→=N2→ Given, a→×b→×c→×d→=0→ ⇒N2→×N2→=0 Hence,…

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

Explore more questions on app

From TS EAMCET

Explore more questions on app