If `bar(A)=2bar(i)-3bar(j)+4bar(k)` ,its component in `x` -y plane is

If A = 2i - 3j + 4k, its component in xy plane is

In the circle shown above, O is the center and bar(AB) is a diameter . There are two semicircles with diameters bar(AO) and bar(BO) , and four smaller semicircles with congruent diameters bar(AC), bar(CO),bar(OD) and bar(DB) . A point is picked at random in the large circle . What is the probability that it lands in a shaded region ?

A force 2bar(i)+bar(j)-bar(k) Newton acts on a body which is initially at rest . At the end of 20 seconds the velocity of the body is 4bar(i)+2bar(j)-2bar(k) m/s . What is the mass of the body ?

A rectangular plate in the x-y plane is shown in the figure. A force bar(F) = 2hat(i) - 3 hat(j) N is applied at point B. Find the torque of bar(F) about (a) the origin O (b) the point C (c) X-axis, Y-axis and Z-axis.

Parallelogram ABCD is graphed in the standard (x,y) coordinate plane below. Sides bar(AB) and bar(CD) are each sqrt(10) coordinate units long. Sides bar(AD) and bar(BC) are each 5 coordinate unit long. The distance between bar(AD) and bar(BC) is 3 coordinate units. What is the distance, in coordinate units, from B to D?

Show that points with p.v bar(a)-2bar(b)+3bar(c ),-2bar(a)+3bar(b)-bar(c ),4bar(a)-7bar(b)+7bar(c ) are collinear. It is given that vectors bara,barb,bar c are non-coplanar.

Let O be the origin and let PQR be an arbitrary triangle. The point S is such that bar(OP)*bar(OQ)+bar(OR)*bar(OS)=bar(OR)*bar(OP)+bar(OQ)*bar(OS)=bar(OQ)*bar(OR)+bar(OP)*bar(OS) Then the triangle PQR has S as its

Parallelogram ABCD is graphed in the standard (x,y) coordinate plane below. Sides bar(AB) and bar(CD) are each sqrt(10) coordinate units long. Sides bar(AD) and bar(BC) are each 5 coordinate unit long. The distance between bar(AD) and bar(BC) is 3 coordinate units. Parallelogram ABCD will be reflected over the y-axis. what will be the coordinates of the image of A?

Parallelogram ABCD is graphed in the standard (x,y) coordinate plane below. Sides bar(AB) and bar(CD) are each sqrt(10) coordinate units long. Sides bar(AD) and bar(BC) are each 5 coordinate unit long. The distance between bar(AD) and bar(BC) is 3 coordinate units. What is the area, in square coordinate units, of ABCD ?

In a regular hexagon ABCDEF, bar(AB) + bar(AC)+bar(AD)+ bar(AE) + bar(AF)=k bar(AD) then k is equal to