Show that if P, A, B are any three points, then `lambda vec(PA)+mu vec(PB)=(lambda + mu)vec(PC`, where C divides [AB] in the ratio `mu : lambda`.

Let ABCDE be a regular pentagon.If vec OD=vec OA+lambdavec OB+muvec OC, where O is the origin,then mu-lambda

The magnitude of the vectors vec(a) and vec(b) are equal and the angle between them is 60^(@) . If the vectors lambda vec(a)+vec(b) and vec(a)-lambda vec(b) are perpendicular to each other, then what is the value of lambda ?

The vector equation of the plane passing through the origin and the line of intersection of the planes vec rdot vec a=lambdaa n d vec rdot vec b=mu is a. vec rdot(lambda vec a-mu vec b)=0 b. vec rdot(lambda vec b-mu vec a)=0 c. vec rdot(lambda vec a+mu vec b)=0 d. vec rdot(lambda vec b+mu vec a)=0

If vec a,vec b and vec c be any three vectors then show that vec a+(vec b+vec c)=(vec a+vec b)+vec c

Write the equation of the plane vec r= vec a+lambda vec b+mu vec c\ in scalar product form.

Show that equation of the plane passing through a point having position vector vec(a) and parallel to vec(b) and vec(c) is vec(r) = vec(a) + lambda vec(b) + mu vec(c) .

Write the equation of the plane containing the lines vec r= vec a+lambda vec b\ a n d\ vec r= vec a+mu vec c

If the points A(-1, 3, lambda), B(-2, 0, 1) and C(-4, mu, -3) are collinear, then the values of lambda and mu are

vec a = hat i + hat j + hat k, vec b = hat i + hat j, vec c = hat i and (vec a * vec b) * vec c = lambdavec a + muvec b then show that lambda + mu = 0

Write the position vector of the point where the line vec r= vec a+lambda vec b meets the plane vec r dot (vec n)=0.