( r i )( i r )+( r j )( j r )+( r k )( k r )=
Mathematics · JEE Advanced · NTA Exams — Three Dimensional Geometry
\((\overrightarrow{\mathbf{r}} \cdot \hat{\mathbf{i}})(\hat{\mathbf{i}} \times \overrightarrow{\mathbf{r}})+(\overrightarrow{\mathbf{r}} \cdot \hat{\mathbf{j}})(\hat{\mathbf{j}} \times \overrightarrow{\mathbf{r}})+(\overrightarrow{\mathbf{r}} \cdot \hat{\mathbf{k}})(\hat{\mathbf{k}} \times \overrightarrow{\mathbf{r}})=\)
- 0
- \(\overrightarrow{\mathrm{r}}\)
- \(2 \vec{r}\)
- \(3 \overrightarrow{\mathrm{r}}\)
Answer
(A) 0
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- Let A ( a ) and B ( b ) be points on two skew lines r = a + p and r = b + u q and the shortest distance…
- A line with positive direction cosines passes through the point P (2, –1, 2) and makes equal angles with the…
- The point P is the intersection of the straight line joining the points Q (2, 3, 5) and R (1, –1, 4) with the…
- If P 1 : r n _ 1 - d 1 = 0, P 2 : r n _ 2 – d 2 = 0 and P 3 : r n _ 3 – d 3 = 0 are three planes and n _ 1 …
- In R 3 , let L be a straight line passing through the origin. Suppose that all the points on L are at a…
- Assertion : Let a , ~b , c and d are position vectors of four points A, B, C and D and 3 a -2 ~b +5 c -6 ~d =…
- If a , ~b , c are such that [ array lll a & b & c array ]=1, c = a b , a ~b < 2 3 and | a |= 2 ,| ~b |= 3 , |…
- Assertion : Let a =2 i +3 j - k , b =4 i +6 j -2 k , then a b = o Reason : If a o , b o and a and b are…
More Three Dimensional Geometry questions · Browse all practice questions