If → a, → b, → c are three mutually perpendicular vectors of equal magnitude, prove that (→ a + → b + → c) is equally inclined with vectors → a, → b and → c. View Solution Q 2

lf a vector ¯ ¯¯ ¯ A = 2 ¯ i + 2 ¯ j + 3 ¯ ¯ ¯ k and ¯ ¯¯ ¯ B = 3 ¯ i + 6 ¯ j + n ¯ ¯ ¯ k, are perpendicular to each other, then the value of 'n' is: View Solution

The sum and difference of two perpendicular vectors of equal length are. Perpendicular to each other and of equal length; Of equal length and have an obtuse angle between them; …

If A and B are two perpendicular vectors given by ¯ ¯¯ ¯ A = 5 ¯ i + 7 ¯ j + 3 ¯ ¯ ¯ k, and 4 ¯ ¯¯ ¯ B = 2 ¯ i + 2 ¯ j + c ¯ ¯ ¯ k, then the value of c is: View Solution Q 2

(i) Find a unit vector perpendicular to both the vectors 4 i ^-j ^ + 3 k ^ and-2 i ^ + j ^-2 k ^. (ii) Find a unit vector perpendicular to the plane containing the vectors a → = 2 i ^ + j ^ + k ^ and b → = …

Find a unit vector perpendicular to each of the vectors 2 → a + → b and → a − 2 → b, where → a = ˆ i + 2 ˆ j − ˆ k, → b = ˆ i + ˆ j + ˆ k. View Solution

Identify two pairs of perpendicular vectors in the expression. Show diagrammatically the orientation of the dipole in the field for which the torque is (i) Maximum (ii) Half the maximum …

(i) Find a unit vector perpendicular to both the vectors 4 i ^-j ^ + 3 k ^ and-2 i ^ + j ^-2 k ^. (ii) Find a unit vector perpendicular to the plane containing the vectors a → = 2 i ^ + j ^ + k ^ and b → = …

Find a vector of magnitude 6 which is perpendicular to both the vectors → a = 4 ^ i − ^ j + 3 ^ k and → b = − 2 ^ i + ^ j − 2 ^ k. Open in App Solution

Vectors 3 → a − 5 → b and 2 → a + → b are mutually perpendicular. If → a + 4 → b and → b − → a are also mutually perpendicular, then the cosine of the angle between → a and → b is