Find a vector in the direction of vector →a=i^−2j^that has magnitude 7 units.
Let a,bandc be unit vectors such that a+b−c=0. If the area of triangle formed by vectors aandbisA, then what is the value of 4A2?
The vector a has the components 2p and 1 w.r.t. a rectangular Cartesian system. This system is rotated through a certain angel about the origin in the counterclockwise sense. If, with respect to a new system, a has components (p+1)and1 , then p is equal to a. −4 b. −1/3 c. 1 d. 2
If 4i^+7j^+8k^,2i^+3j^+24and2i^+5j^+7k^ are the position vectors of the vertices A,BandC, respectively, of triangle ABC , then the position vecrtor of the point where the bisector of angle A meets BC is a. 32(−6i^−8j^−k^) b. 32(6i^+8j^+6k^) c. 31(6i^+13j^+18k^) d. 31(5j^+12k^)
If the vectors i^−j^,j^+k^anda form a triangle, then a may be a. −i^−k^ b. i^−2j^−k^ c. 2i^+j^+k^ d. i^+k^
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
If vectors a=i^+2j^−k^,b=2i^−j^+k^andc=lambdai^+j^+2k^ are coplanar, then find the value of (λ−4)˙
ABCD is a tetrahedron and O is any point. If the lines joining O to the vrticfes meet the opposite faces at P,Q,RandS, prove that APOP+BQOQ+CROR+DSOS=1.