If a , b , c are three non-zero non-coplanar vectors and b _ 1 = b - a b | a |^ 2 a , b _…
Physics · JEE Advanced · NTA Exams — Kinematics
If \(\vec{a}, \vec{b}, \vec{c}\)are three non-zero non-coplanar vectors and
\(\vec{b}_{1}=\vec{b}-\frac{\vec{a} \cdot \vec{b}}{|\vec{a}|^{2}} \vec{a}, \vec{b}_{2}=\vec{b}+\frac{\vec{a} \cdot \vec{b}}{|\vec{a}|^{2}} \vec{a}\)
\(\vec{c}_{1}=\vec{c}-\frac{\vec{c} \cdot \vec{a}}{|\vec{a}|^{2}} \vec{a}-\frac{\vec{b} \cdot \vec{c}^{2}}{|\vec{c}|^{2}} \vec{b}_{1},\) \(\vec{c}_{2}=\vec{c}-\frac{\vec{c} \cdot \vec{a}}{|\vec{a}|^{2}} \vec{a}-\frac{\vec{b}_{1} \cdot \vec{c}^{2}}{\left|\vec{b}_{1}\right|^{2}} \vec{b}_{1}\)
\(\vec{c}_{3}=\vec{c}-\frac{\vec{c} \cdot \vec{a}}{|\vec{c}|^{2}} \vec{a}+\frac{\vec{b} \cdot \vec{c}}{|\vec{c}|^{2}} \vec{b}_{1},\) \(\vec{c}_{4}=\vec{c}-\frac{\vec{c} \cdot \vec{a}}{|\vec{c}|^{2}} \vec{a}-\frac{\vec{b} \cdot \vec{c}}{|\vec{b}|^{2}} \vec{b}_{1},\)
then the set of orthogonal vectors is
\(\vec{b}_{1}=\vec{b}-\frac{\vec{a} \cdot \vec{b}}{|\vec{a}|^{2}} \vec{a}, \vec{b}_{2}=\vec{b}+\frac{\vec{a} \cdot \vec{b}}{|\vec{a}|^{2}} \vec{a}\)
\(\vec{c}_{1}=\vec{c}-\frac{\vec{c} \cdot \vec{a}}{|\vec{a}|^{2}} \vec{a}-\frac{\vec{b} \cdot \vec{c}^{2}}{|\vec{c}|^{2}} \vec{b}_{1},\) \(\vec{c}_{2}=\vec{c}-\frac{\vec{c} \cdot \vec{a}}{|\vec{a}|^{2}} \vec{a}-\frac{\vec{b}_{1} \cdot \vec{c}^{2}}{\left|\vec{b}_{1}\right|^{2}} \vec{b}_{1}\)
\(\vec{c}_{3}=\vec{c}-\frac{\vec{c} \cdot \vec{a}}{|\vec{c}|^{2}} \vec{a}+\frac{\vec{b} \cdot \vec{c}}{|\vec{c}|^{2}} \vec{b}_{1},\) \(\vec{c}_{4}=\vec{c}-\frac{\vec{c} \cdot \vec{a}}{|\vec{c}|^{2}} \vec{a}-\frac{\vec{b} \cdot \vec{c}}{|\vec{b}|^{2}} \vec{b}_{1},\)
then the set of orthogonal vectors is
Answer
(B)
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- A particle P is projected from a point on the surface of smooth inclined plane (see figure). Simultaneously…
- If the displacement of a particle varies with time as x = t + 7, the
- The center of a disk of radius r and mass m is attached to a spring of spring constant k , inside a ring of…
- A person walks up a stationary escalator in time t1. If he remains stationary on the moving escalator, then…
- If a , b and c are unit vectors, then | a - b |^ 2 +| b - c |^ 2 +| c - a |^ 2 does not exceed
- Time taken by an object falling from rest to cover the height of h 1 and h 2 is respectively t1 and t2 then…
- The equation of motion of a projectile is y=12 x- 3 4 x^ 2 . Given that g =10 ms–2, what is the range of the…
- Assertion: Two stones are simultaneously projected from level ground from same point with same speeds but…