Related InterviewSolutions

• If c is a unit vector perpendicular to the vectors a and b, write another unit vector perpendicular to a and b.
• If the vectors i - 2xj + 2yk and i + 2xj - 3yk are perpendicular, then the locus of (x , y) is A. a circleB. an ellipseC. a hyperbolaD. none of these
• If a and b are two vectors such that vector a.b = 6, |a| = 3 and |b| = 4 Write the projection of on
• What vector a and b is the angle between vectors and with magnitudes 2 and √3 respectively? Given vector a.b = √3.
• If vectors a, b represent the diagonals of a rhombus, thenA. \(\vec a\times\vec b=\vec 0\)B. \(\vec a.\vec b=0\)C. \(\vec a.\vec b=1\)D. \(\vec a\times\vec b=\vec a\)
• Find the projection of vector (8i + j) in the direction of vector (i + 2j - 2k).
• Prove that vectors (a + b).(a - b) = |a|2 + |b|2 ⇔ a⊥b, where vectors a ≠ 0 and  vectors b ≠ 0.
• Write the number of vectors of unit length perpendicular to both the vectors a = 2i + j + 2k and b = j + k.
• Write the angle between the vectors a x b and b x a.
• If a,  b,  c are three unit vectors such that a x b = c, b x c = a, c x a = b. show that a, b, c, form an orthonormal right handed traid of unit vectors.