If either a=0or b=0, then a⋅b=0But the converse need not be true. Justify your answer with an example.
Four non –zero vectors will always be a. linearly dependent b. linearly independent c. either a or b d. none of these
The position vectors of the vertices A,BandC of a triangle are three unit vectors a,b,andc, respectively. A vector d is such that da˙=db˙=dc˙andd=λ(b+c)˙ Then triangle ABC is a. acute angled b. obtuse angled c. right angled d. none of these
Let r1,r2,r3,,rn be the position vectors of points P1,P2,P3,Pn relative to the origin O˙ If the vector equation a1r1+a2r2++anrn=0 hold, then a similar equation will also hold w.r.t. to any other origin provided a. a1+a2++˙an=n b. a1+a2++˙an=1 c. a1+a2++˙an=0 d. a1=a2=a3+˙an=0
A vector has components p and 1 with respect to a rectangular Cartesian system. The axes are rotted through an angel αabout the origin the anticlockwise sense. Statement 1: IF the vector has component p+2and 1 with respect to the new system, then p=−1. Statement 2: Magnitude of the original vector and new vector remains the same.
Let a,bandc be three units vectors such that 2a+4b+5c=0. Then which of the following statement is true? a. a is parallel to b b. a is perpendicular to b c. a is neither parallel nor perpendicular to b d. none of these