Mathematics Tes...

Find a unit vector parallel to the vector -2î + 3ĵ.

The direction cosines of the line that makes equal angles with three axes in a space are

If \(\vec r = ​​\vec A_1 + \lambda \vec B_1 \) and \(\vec r = ​​\vec A_2 + \lambda \vec B_2 \) are intersecting lines then which of the following is correct?

There are 2 vectors \(\rm \vec a\)= i + 2j + k and \(\rm \vec b\) = -i + j - 3k. Find the projection of \(\rm \vec a\) on \(\rm \vec b\)

If a, b, c are non-coplanar then find the value of 2[a b c] + [b a c] =

If the straight line \(\frac{x-x_0}{l}=\frac{y-y_0}{m}=\frac{z-z_0}{n}\) is parallel to the plane ax + by + cz + d = 0, then which one of the following is correct?

If \(|\vec a|\) = 3, \(\left| {\vec b} \right| = 4\) and \(\left| {\vec a - \vec b} \right| = 5,\) then what is the value of \(\left| {\vec a + \vec b} \right|\)?

Find the value of k for which the line through the points (2, 4, 8) and (1, 2, 4) is parallel to the line through the points (3, 6, k) and (1, 2, 1) ?

If the vectors \(\widehat i + 2\widehat j + 3\widehat k\), \(λ \widehat i + 4\widehat j + 7\widehat k\), \(- 3\widehat i - 2\widehat j - 5\widehat k\) are collinear if λ equals

In what ratio is the line segment joining the point (−2, −3) and (3, 7) divided by y-axis ?