Show that the vector `hat(i) +hat(j)+hat(k)` is equally inclined to the axes OX,OY and OZ.

Show that the direction cosines of a vector equally inclined to the axes OX,OY and OZ are +-((1)/(sqrt(3)),(1)/(sqrt(3)),(1)/(sqrt(3))) .

Write the projection of the vector hat(i) + hat(j) + hat(k) along the vector hat(j) .

Show that the vectors bar(a) = 2 hat(i) - 3 hat(j) + 4 hat(k) and bar(b) = -4 hat(i) + 6 hat(j) - 8k are collinear.

Show that the vectors 2hat(i)-3hat(j)+4hat(k) and -4hat(i)+6hat(j)-8hat(k) are collinear.

The value of p such that the vectors hat(i) + 3hat(j) - 2hat(k), 2hat(i) - hat(j) + 4hat(k) and 3hat(i) + 2hat(j) + p hat(k) are coplanar is

The scalar product of the vector vec(a) = hat(i) + hat(j) + hat(k) with a unit vector along the sum of vectors vec(b) = 2hat(i) + 4hat(j) - 5hat(k) and vec(c ) = lambda hat(i) + 2hat(j) + 3hat(k) is equal to one. Find the value of lambda and hence find the unit vector along vec(b) + vec(c ) .

Show that the vectors 2hat(i)-hat(j)+hat(k),hat(i)-3hat(j) . And 3hat(i)-4hat(j)-3hat(k) . Form the vertices of a right angled triangle.

Find the sine of the angle between the vectors hat(i) + 2 hat(j) + 2 hat(k) and 3 hat(i) + 2 hat(j) + 6 hat(k)

Write the projection of the vector 7hat(i) + hat(j) - 4hat(k) on the vector 2hat(i) + 6hat(j) + 3hat(k) .

Write a vector in the direction of the vector hat(i) - 2hat(j) + 2hat(k) that has magnitude 9 units.