AP EAMCET · Maths · Three Dimensional Geometry

Angle made by the position vector of the point $(5, - 4, - 3)$ with the positive direction of $X -$ axis is

A $\frac{π}{2}$
B $\frac{π}{6}$
C $\frac{π}{4}$
D $\frac{π}{3}$

Verified Solution

Answer & Solution

Correct Answer

(C) $\frac{π}{4}$

Step-by-step Solution

Detailed explanation

The position vector of the point 5, -4, -3 is 5i^-4j^-3k^ We know that i^ is the unit vector along x-axis So, the angle between the vector 5i^-4j^-3k^ and x-axis will be same as the angle between the vector 5i^-4j^-3k^ and i^. Let the angle be θ…

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.

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Angle made by the position vector of the point (5,-4,-3) with the positive direction of X-axis is

Step-by-step Solution

Angle made by the position vector of the point $(5, - 4, - 3)$ with the positive direction of $X -$ axis is