Show that each of the given three vectors is a unit vector: 71(2i^+3j^+6k^),71(3i^−6j^+2k^),71(6i^+2j^−3k^)Also, show that they are mutually perpendicular to each other.
Let a,b,andcanda′,b′,c′ are reciprocal system of vectors, then prove that a′×b′+b′×c′+c′×a′=[abc]a+b+c .
Statement 1: If ∣∣a+b∣∣=∣∣a−b∣∣, then a and b are perpendicular to each other. Statement 2: If the diagonal of a parallelogram are equal magnitude, then the parallelogram is a rectangle.
If xandy are two non-collinear vectors and ABC isa triangle with side lengths a,b,andc satisfying (20a−15b)x+(15b−12c)y+(12c−20a)(×xy)=0, then triangle ABC is a. an acute-angled triangle b. an obtuse-angled triangle c. a right-angled triangle d. an isosceles triangle
The vectors 2i+3j^,5i^+6j^ and 8i^+λj^ have initial points at (1, 1). Find the value of λ so that the vectors terminate on one straight line.
The position vectors of the vertices A,B,andC of a triangle are i^+j^,j^+k^andi^+k^ , respectively. Find the unite vector r^ lying in the plane of ABC and perpendicular to IA,whereI is the incentre of the triangle.
ABC is a triangle and P any point on BC. if PQ is the sum of AP + PB +PC , show that ABPQ is a parallelogram and Q , therefore , is a fixed point.