Question 6: If the scalar and vector products of two vectors A and B are equal in magnitude, then the angle between the two vectors is
A$45^\circ$
B$90^\circ$
C$180^\circ$
D$360^\circ$
Answer & Solution
Correct answer: A. $45^\circ$
Given A.B = A×B
$$
\Rightarrow \text{AB cos } \theta = \text{AB sin } \theta
$$
$$
\Rightarrow \tan \theta = 1
$$
$$
\Rightarrow \theta = 45^\circ
$$
Hence option a is the answer.
Related questions
The angle θ between two PLANES with normals n1 and n2 satisfies:A point R divides the line joining P (position vector a) and Q (position vector b) INTERNAFor direction cosines l, m, n of any line in 3D:The Cartesian equation of a plane with intercepts 2, 3, 6 on the x, y, z axes is:The vector triple product a × (b × c) simplifies via:The scalar triple product [a b c] geometrically represents:A UNIT VECTOR in the direction of v = 3i + 4j is:Two non-zero vectors a and b are PERPENDICULAR if and only if: