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Show that the points A(1, 2, 7), B(2, 6, 3) and C(3, 10, –1) are collinear.
Given points are A (1, 2, 7), B (2, 6, 3) and C (3, 10, -1)
∴ The given points A, B and C are collinear.
Find the angle between two vectors with magnitudes √3 and 2 respectively having
Find the angle between the vectors
Find the projection of the vector on the vector
Show that each of the given three vectors is a unit vector:
Also, show that they are mutually perpendicular to each other.
Evaluate the product
Find the magnitude of two vectors , having the same magnitude and such that the angle between them is 60° and their scalar product is 1/2.
Find if for a unit vector
If are such that is perpendicular to then find the value of λ.
Show that is perpendicular to for any two nonzero vectors .
If and then what can be concluded about the vector
If are unit vectors such that find the value of
If either vector then But the converse need not be true. Justify your answer with an example.
If the vertices A, B, C of a triangle ABC are (1, 2, 3), (–1, 0, 0), (0, 1, 2), respectively, then find ∠ABC, [∠ABC is the angle between the vectors ].
Show that the vectors form the vertices of a right angled triangle.
If is a nonzero vector of magnitude ‘a’ and λ a nonzero scalar, then is unit vector if