`(2 hat i . 3 hat j )` =

The component of the vector [barA = (2hat i + 3 hat j)] along the vector [bar B = (hat i + hat j)] is

Show that the following points whose position vectors are given are collinear : (i) 5 hat(i) + 5 hat(k), 2 hat(i) + hat(j) + 3 hat(k) and - 4 hat(i) + 3 hat(j) - hat(k) (ii) - 2 hat(i) + 3 hat(j) + 5 hat(k), hat(i) + 2 hat(j) + 3 hat(k) and 7 hat(i) - hat(k) .

The unit vector along vec A=2hat i+3hat j is: (A) 2hat i+3hat j(B)(2hat i+3hat j)/(2)(C)(2hat i+3hat j)/(13) (D) (2hat i+3hat j)/(sqrt(13))

The vector equation of the plane which is perpendicular to 2hat i-3hat j+hat k=0 and at a distance of 5units from the origin is (A)vec r*(2hat i-3hat j+k)=5sqrt(14)(B)vec r*(2hat i-3hat j+k)=5(C)vec r*(2hat i-3hat j+k)/(sqrt(14)) (D) (vec r*(2hat i+3hat j+k))/(sqrt(14))

Show that the points A(-2hat i+3hat j+5hat k),B(hat i+2hat j+3hat k) and C(7hat i-hat k) are collinear.

If the position vectors of the points A, B, C are -2hat i + 2hat j + 2hat k, 2hat i+ 3hat j +3hat k and -hat i 2hat j+3hat k respectively, show that ABC is an isosceles triangle.

Find bar(a). bar(b) xx bar(c) , if bar(a) = 3 hat(i) - hat(j) + 4 hat(k), bar(b) = 2hat(i) + 3 hat(j) - hat(k), bar(c) = - 5 hat(i) + 2 hat(j) + 3 hat(k)

A vector ? is perpendicular to the vectors 2hat i+3hat j-hat k,hat i-2hat j+3hat k and satisfies the condition vectors vec c*(2hat i-hat j+hat k)+6=0 FInd the vector vec c