7 Show that the vectors coplanar if are coplanar
6 Find x such that the four points A (3, 2, 1) B (4, x, 5), C (4, 2, –2) and D (6, 5, –1) are coplanar.
5 Show that the four points with position vectors and are coplanar.
4(b) Let Then
If and show that no value of can make coplanar.
4 (a) Let Then
If and find which makes coplanar
3. Find if the vectors are coplanar.
2. Show that the vectors are coplanar.
Q19 Choose the correct. If is the angle between any two vectors , then when
is equal to
Q18 The value of is
Q17 Choose the correct answer. Let be two unit vectors and is the angle between them. Then is a unit vector if
Q.14 If are mutually perpendicular vectors of equal magnitudes, show that the vector is equally inclined to .
Q16 Choose the correct answer If is the angle between two vectors , then only when
Q15 Prove that , if and only if are perpendicular, given
Q13 The scalar product of the vector with a unit vector along the sum of vectors and is equal to one. Find the value of .
Q12 Let . Find a vector which is perpendicular to both
Q11 Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are
Q10 The two adjacent sides of a parallelogram are . Find the unit vector parallel to its diagonal. Also, find its area.
Q9 Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are externally in the ratio 1: 2. Also, show that P is the mid point of the line segment RQ.
Q8 Show that the points A(1, – 2, – 8), B(5, 0, –2) and C(11, 3, 7) are collinear, and find the ratio in which B divides AC.