KCET 2021

The equation of the line joining the points \((-3,4,11)\) and \((1,-2,7)\) is

The angle between the lines whose direction cosines are \(\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2}\right)\) and \(\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{-\sqrt{3}}{2}\right)\)

The mid points of the sides of triangle are \((1,5,-1)(0,4,-2)\) and \((2,3,4)\) then centroid of the triangle

The area of the quadrilateral \(A B C D\) when \(A(0,4,1), B(2,3,-1), C(4,5,0)\) and \(D(2,6,2)\) is equal to

The value of \(\tan 1^{\circ} \tan 2^{\circ} \tan 3^{\circ} \ldots \tan 89^{\circ}\) is

The value of \(\cos 1200^{\circ}+\tan 1485^{\circ}\) is

If the area of the parallelogram with \(\mathbf{a}\) and \(\mathbf{b}\) as two adjacent sides is 15 sq units, then the area of the parallelogram having \(\mathrm{3 a+2 b}\) and \(\mathbf{a}+3 \mathbf{b}\) as two adjacent sides in sq units i...

A vector a makes equal acute angles on the coordinate axis. Then the projection of vector \(\mathbf{b}=5 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) on \(\mathbf{a}\) is

If \(\mathbf{a} \cdot \mathbf{b}=0\) and \(\mathbf{a}+\mathbf{b}\) makes an angle \(60^{\circ}\) with \(a\), then

The diagonals of a parallelogram are the vectors \(3 \hat{\mathbf{i}}+6 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}\). and \(-\hat{\mathbf{i}}-2 \hat{\mathbf{j}}-8 \hat{\mathbf{k}}\). Then the length of the shorter side of parallelogram is