Magnitude of the vector 2i – 2j – k is
: (A) 4
(B) 3
(C) 2
(D) 1​

Area of a rectangle having vertices A, B, C and D with position vectors - hat i+1/2 hat j+4 hat k , hat i+1/2 hat j+4 hat k , hat i-1/2 hat j+4 hat k and - hat i-1/2 hat j+4 hat k respectively is (A) 1/2 (B) 1 (C) 2 (D) 4

Let vec a = hat i + hat j + hat k, vec b = hat i + 4 hat j - hat k, vec c = hat i + hat j + 2 hat k and hat s be a the unit vector the magnitude of the vector (vec a .vec s)(vec b xx vec c) + (vec b. vec s)(vec c xx vec a) + ( vec c.vec s)(vec a xx vec b) is equal to (A) 1 (B) 2 (C) 3 (D) 4

The positon vector of the centroid of the triangle ABC is 2i+4j+2k . If the position vector of the vector A is 2i+6j+4k., then the position vector of midpointof BC is (A) 2i+3j+k (B) 2i+3jk (C) 2i-3j-k (D) -2i-3j-k

I.(i) If vec a=2hat i+4hat j-4hat k,vec b=-5hat i+4hat j+2hat k and vec c=3hat i-3hat j-2hat k then find the magnitude of the vector vec a+vec b+2vec c and a unit vector in the direction of this vector.

The magnitude of the vector product of the vector hat i+hat j+hat k with a unit vector along the sum of vectors 2hat i+4hat j-5hat k and lambda i+2hat j+3hat k is equal to sqrt(2). Find the value of lambda_(.)

The magnitude of the vector hat(i)+xhat(j)+3hat(k) is half of the magnitude of vector 4hat(i)+(4x-2)hat(j)+2hat(k) . The values of x are ?

Find a vector of magnitude 6 which is perpendicular to both the vectors vec(a)= 4 hat(i)-hat(j) + 3 hat(k) and vec(b) = -2 hat(i) + hat(j)- 2 hat(k).

A vector c perpendicular to the vectors 2i+3j-k" and "i-2j+3k satisfying c.(2i-j+k)=-6 is

Consider the vectors a = i- 2j + k and b= 4i- 4j + 7k What is the vector perpendicular to both the vectors?