The component of the vector A = 2i + 3j along the vector i + j is

The angle which the vector A = 2i + 3j makes with the y axis, where i and j are unit vectors along x and y axes, respectively, is

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Show that vector a = 3i - 2j + k , vector b = i - 3j + 5k and vector c = 2i + j - 4k forms a right angled triangle?

i and j are unit vectors along x- and y-axis respectively. What is the magnitude and direction of the vectors i + j and i− j ? What are the components of a vector A = 2i and 3j along the directions of i + j and i – j ? [You may use graphical method]